Satellite Sampling and Retrieval Errors in Regional Monthly Rain Estimates from TMI AMSR-E, SSM/I, AMSU-B and the TRMM PR

Passive and active microwave rain sensors onboard earth-orbiting satellites estimate monthly rainfall from the instantaneous rain statistics collected during satellite overpasses. It is well known that climate-scale rain estimates from meteorological satellites incur sampling errors resulting from the process of discrete temporal sampling and statistical averaging. Sampling and retrieval errors ultimately become entangled in the estimation of the mean monthly rain rate. The sampling component of the error budget effectively introduces statistical noise into climate-scale rain estimates that obscure the error component associated with the instantaneous rain retrieval. Estimating the accuracy of the retrievals on monthly scales therefore necessitates a decomposition of the total error budget into sampling and retrieval error quantities. This paper presents results from a statistical evaluation of the sampling and retrieval errors for five different space-borne rain sensors on board nine orbiting satellites. Using an error decomposition methodology developed by one of the authors, sampling and retrieval errors were estimated at 0.25 resolution within 150 km of ground-based weather radars located at Kwajalein, Marshall Islands and Melbourne, Florida. Error and bias statistics were calculated according to the land, ocean and coast classifications of the surface terrain mask developed for the Goddard Profiling (GPROF) rain algorithm. Variations in the comparative error statistics are attributed to various factors related to differences in the swath geometry of each rain sensor, the orbital and instrument characteristics of the satellite and the regional climatology. The most significant result from this study found that each of the satellites incurred negative longterm oceanic retrieval biases of 10 to 30%

A Quantum Monte Carlo Method at Fixed Energy

In this paper we explore new ways to study the zero temperature limit of quantum statistical mechanics using Quantum Monte Carlo simulations. We develop a Quantum Monte Carlo method in which one fixes the ground state energy as a parameter. The Hamiltonians we consider are of the form $H=H_{0}+\lambda V$ with ground state energy E. For fixed $H_{0}$ and V, one can view E as a function of $\lambda$ whereas we view $\lambda$ as a function of E. We fix E and define a path integral Quantum Monte Carlo method in which a path makes no reference to the times (discrete or continuous) at which transitions occur between states. For fixed E we can determine $\lambda(E)$ and other ground state properties of H

Comparisons of Reflectivities from the TRMM Precipitation Radar and Ground-Based Radars

Given the decade long and highly successful Tropical Rainfall Measuring Mission (TRMM), it is now possible to provide quantitative comparisons between ground-based radars (GRs) with the space-borne TRMM precipitation radar (PR) with greater certainty over longer time scales in various tropical climatological regions. This study develops an automated methodology to match and compare simultaneous TRMM PR and GR reflectivities at four primary TRMM Ground Validation (GV) sites: Houston, Texas (HSTN); Melbourne, Florida (MELB); Kwajalein, Republic of the Marshall Islands (KWAJ); and Darwin, Australia (DARW). Data from each instrument are resampled into a three-dimensional Cartesian coordinate system. The horizontal displacement during the PR data resampling is corrected. Comparisons suggest that the PR suffers significant attenuation at lower levels especially in convective rain. The attenuation correction performs quite well for convective rain but appears to slightly over-correct in stratiform rain. The PR and GR observations at HSTN, MELB and KWAJ agree to about 1 dB on average with a few exceptions, while the GR at DARW requires +1 to -5 dB calibration corrections. One of the important findings of this study is that the GR calibration offset is dependent on the reflectivity magnitude. Hence, we propose that the calibration should be carried out using a regression correction, rather than simply adding an offset value to all GR reflectivities. This methodology is developed towards TRMM GV efforts to improve the accuracy of tropical rain estimates, and can also be applied to the proposed Global Precipitation Measurement and other related activities over the globe

Clarification of the circulatory patho-physiology of anaesthesia - Implications for high-risk surgical patients

AbstractThe paper examines the effects of anaesthesia on circulatory physiology and their implications regarding improvement in perioperative anaesthetic management. Changes to current anaesthetic practice, recommended recently, such as the use of flow monitoring in high risk patients, are already beginning to have an impact in reducing complications but not mortality [1]. Better understanding of the patho-physiology should help improve management even further. Analysis of selected individual clinical trials has been used to illustrate particular areas of patho-physiology and how changes in practice have improved outcome. There is physiological support for the importance of achieving an appropriate rate of oxygen delivery (DO2), particularly following induction of anaesthesia. It is suggested that ensuring adequate DO2 during anaesthesia will avoid development of oxygen debt and hence obviate the need to induce a high, compensatory, DO2 in the post-operative period. In contrast to the usual assumptions underlying strategies requiring a global increase in blood flow [1] by a stroke volume near maximization strategy, blood flow control actually resides entirely at the tissues not at the heart. This is important as the starting point for understanding failed circulatory control as indicated by ‘volume dependency’. Local adjustments in blood flow at each individual organ – auto-regulation – normally ensure the appropriate local rate of oxygen supply, i.e. local DO2. Inadequate blood volume leads to impairment of the regulation of blood flow, particularly in the individual tissues with least capable auto-regulatory capability. As demonstrated by many studies, inadequate blood flow first occurs in the gut, brain and kidney. The inadequate blood volume which occurs with induction of anaesthesia is not due to blood volume loss, but probably results from redistribution due to veno-dilation. The increase in venous capacity renders the existing blood volume inadequate to maintain venous return and pre-load. Blood volume shifted to the veins will, necessarily, also reduce the arterial volume. As a result stroke volume and cardiac output fall below normal with little or no change in peripheral resistance. The resulting pre-load dependency is often successfully treated with colloid infusion and, in some studies, ‘inotropic’ agents, particularly in the immediate post-operative phase. Treatment during the earliest stage of anaesthesia can avoid the build up of oxygen debt and may be supplemented by drugs which maintain or restore venous tone, such as phenylephrine; an alternative to volume expansion. Interpretation of circulatory patho-physiology during anaesthesia confirms the need to sustain appropriate oxygen delivery. It also supports reduction or even elimination of supplementary crystalloid maintenance infusion, supposedly to replace the “mythical” third space loss. As a rational evidence base for future research it should allow for further improvements in anaesthetic management

Evaluation of TRMM Ground-Validation Radar-Rain Errors Using Rain Gauge Measurements

Ground-validation (GV) radar-rain products are often utilized for validation of the Tropical Rainfall Measuring Mission (TRMM) spaced-based rain estimates, and hence, quantitative evaluation of the GV radar-rain product error characteristics is vital. This study uses quality-controlled gauge data to compare with TRMM GV radar rain rates in an effort to provide such error characteristics. The results show that significant differences of concurrent radar-gauge rain rates exist at various time scales ranging from 5 min to 1 day, despite lower overall long-term bias. However, the differences between the radar area-averaged rain rates and gauge point rain rates cannot be explained as due to radar error only. The error variance separation method is adapted to partition the variance of radar-gauge differences into the gauge area-point error variance and radar rain estimation error variance. The results provide relatively reliable quantitative uncertainty evaluation of TRMM GV radar rain estimates at various times scales, and are helpful to better understand the differences between measured radar and gauge rain rates. It is envisaged that this study will contribute to better utilization of GV radar rain products to validate versatile spaced-based rain estimates from TRMM, as well as the proposed Global Precipitation Measurement, and other satellites

Assessing the Relative Performance of Microwave-based Satellite Rain Rate Retrievals using TRMM Ground Validation Data

Space-borne microwave sensors provide critical rain information used in several global multi-satellite rain products, which in turn are used for a variety of important studies, including landslide forecasting, flash flood warning, data assimilation, climate studies, and validation of model forecast of precipitation. This study employs four years (2003-2006) of satellite data to assess the relative performance and skill of SSM/I (F13, F14 and F15), AMSU-B (N15, N16 and N17), AMSR-E (AQUA) and the TRMM Microwave Imager (TMI) in estimating surface rainfall based on direct instantaneous comparison with ground-based rain estimates from Tropical Rainfall Measuring Mission (TRMM) Ground Validation (GV) sites at Kwajalein, Republic of the Marshall Islands (KWAJ) and Melbourne, Florida (MELB). The relative performance of each of these satellites is examined via comparisons with GV radar-based rain rate estimates. Because underlying surface terrain is known to affect the relative performance of the satellite algorithms, the data for MELB was further stratified into ocean, land and coast categories using a 0.25 terrain mask. Of all the satellite estimates compared in this study, TMI and AMSR-E exhibited considerably higher correlations and skills in estimating/observing surface precipitation. While SSM/I and AMSU-B exhibited lower correlations and skills for each of the different terrain categories, the SSM/I absolute biases trended slightly lower than AMSRE over ocean, where the observations from both emission and scattering channels were used in the retrievals. AMSU-B exhibited the least skill relative to GV in all of the relevant statistical categories, and an anomalous spike was observed in the probability distribution functions near 1.0 mm hr-1. This statistical artifact appears to be related to attempts by algorithm developers to include some lighter rain rates, not easily detectable by its scatter-only frequencies. AMSU-B, however, agreed well with GV when the matching data was analyzed on monthly scales. These results signal developers of global rainfall products, such as the TRMM Multi-Satellite Precipitation Analysis (TMPA), and the Climate Data Center s Morphing (CMORPH) technique, that care must be taken when incorporating data from these input satellite estimates in order to provide the highest quality estimates in their products

Comparisons of Instantaneous TRMM Ground Validation and Satellite Rain Rate Estimates at Different Spatial Scales

This study provides a comprehensive inter-comparison of instantaneous rain estimates from the two rain sensors aboard the TRMM satellite with ground data from thee designated Ground Validation Sites: Kwajalein Atoll, Melbourne, Florida and Houston, Texas. The satellite rain retrievals utilize rain observations collected by the TRMM microwave imager (TMI) and the Precipitation Radar (PR) aboard the TRMM satellite. Three standard instantaneous rain products are the generated from the rain information retrieved from the satellite using the TMI, PR and Combined (COM) rain algorithms. The validation data set used in this study was obtained from instantaneous rain rates inferred from ground radars at each GV site. The first comparison used 0.5(sup 0) x 0.5(sup 0) gridded data obtained from the TRMM 3668 product, and similarly gridded GV data obtained from ground-based radars. The comparisons were made at the same spatial and temporal scales in order to eliminate sampling biases in our comparisons. An additional comparison was made by averaging rain rates for the PR, COM and GV estimates within each TMI footprint (approx. 150 square kilometers). For this analysis, unconditional mean rain rates from PR, COM and GV estimates were calculated within each TMI footprint that was observed within 100 km from the respective GV site (and also observed by the PR). This analysis used all the available matching data from the period 1999-2004, representing a sample size of over 50,000 footprints for each site. In the first analysis our results showed that all of the respective rain rate estimates agree well, with some exceptions. The more salient differences were associated with heavy rain events in which one or more of the algorithms failed to properly retrieve these extreme events. Also, it appears that there is a preferred mode of precipitation for TMI rain rates at or near 2 mm per hour over the ocean. This mode was noted over ocean areas of Melbourne, Florida and Kwajalein, Republic of the Marshall Islands, and is shown to exist in TRMM tropical-global ocean areas as well. Further research by algorithm developers is needed to explain or justify the seemingly errant observed probability distributions

Assessing the Relative Performance of Microwave-Based Satellite Rain Rate Retrievals Using TRMM Ground Validation Data

Space-borne microwave sensors provide critical rain information used in several global multi-satellite rain products, which in turn are used for a variety of important studies, including landslide forecasting, flash flood warning, data assimilation, climate studies, and validation of model forecasts of precipitation. This study employs four years (2003-2006) of satellite data to assess the relative performance and skill of SSM/I (F13, F14 and F15), AMSU-B (N15, N16 and N17), AMSR-E (Aqua) and the TRMM Microwave Imager (TMI) in estimating surface rainfall based on direct instantaneous comparisons with ground-based rain estimates from Tropical Rainfall Measuring Mission (TRMM) Ground Validation (GV) sites at Kwajalein, Republic of the Marshall Islands (KWAJ) and Melbourne, Florida (MELB). The relative performance of each of these satellite estimates is examined via comparisons with space- and time-coincident GV radar-based rain rate estimates. Because underlying surface terrain is known to affect the relative performance of the satellite algorithms, the data for MELB was further stratified into ocean, land and coast categories using a 0.25 terrain mask. Of all the satellite estimates compared in this study, TMI and AMSR-E exhibited considerably higher correlations and skills in estimating/observing surface precipitation. While SSM/I and AMSU-B exhibited lower correlations and skills for each of the different terrain categories, the SSM/I absolute biases trended slightly lower than AMSRE over ocean, where the observations from both emission and scattering channels were used in the retrievals. AMSU-B exhibited the least skill relative to GV in all of the relevant statistical categories, and an anomalous spike was observed in the probability distribution functions near 1.0 mm/hr. This statistical artifact appears to be related to attempts by algorithm developers to include some lighter rain rates, not easily detectable by its scatter-only frequencies. AMSU-B, however, agreed well with GV when the matching data was analyzed on monthly scales. These results signal developers of global rainfall products, such as the TRMM Multi-Satellite Precipitation Analysis (TMPA), and the Climate Data Center s Morphing (CMORPH) technique, that care must be taken when incorporating data from these input satellite estimates in order to provide the highest quality estimates in their products.

Quality Control and Calibration of the Dual-Polarization Radar at Kwajalein, RMI

Weather radars, recording information about precipitation around the globe, will soon be significantly upgraded. Most of today s weather radars transmit and receive microwave energy with horizontal orientation only, but upgraded systems have the capability to send and receive both horizontally and vertically oriented waves. These enhanced "dual-polarimetric" (DP) radars peer into precipitation and provide information on the size, shape, phase (liquid / frozen), and concentration of the falling particles (termed hydrometeors). This information is valuable for improved rain rate estimates, and for providing data on the release and absorption of heat in the atmosphere from condensation and evaporation (phase changes). The heating profiles in the atmosphere influence global circulation, and are a vital component in studies of Earth s changing climate. However, to provide the most accurate interpretation of radar data, the radar must be properly calibrated and data must be quality controlled (cleaned) to remove non-precipitation artifacts; both of which are challenging tasks for today s weather radar. The DP capability maximizes performance of these procedures using properties of the observed precipitation. In a notable paper published in 2005, scientists from the Cooperative Institute for Mesoscale Meteorological Studies (CIMMS) at the University of Oklahoma developed a method to calibrate radars using statistically averaged DP measurements within light rain. An additional publication by one of the same scientists at the National Severe Storms Laboratory (NSSL) in Norman, Oklahoma introduced several techniques to perform quality control of radar data using DP measurements. Following their lead, the Topical Rainfall Measuring Mission (TRMM) Satellite Validation Office at NASA s Goddard Space Flight Center has fine-tuned these methods for specific application to the weather radar at Kwajalein Island in the Republic of the Marshall Islands, approximately 2100 miles southwest of Hawaii and 1400 miles east of Guam in the tropical North Pacific Ocean. This tropical oceanic location is important because the majority of rain, and therefore the majority of atmospheric heating, occurs in the tropics where limited ground-based radar data are available

The XY Model on a Dynamical Random Lattice

We study the XY model on a lattice with fluctuating connectivity. The expectation is that at an appropriate critical point such a system corresponds to a compactified boson coupled to 2d quantum gravity. Our simulations focus, in particular, on the important topological features of the system. The results lend strong support to the two phase structure predicted on the basis of analytical calculations. A careful finite size scaling analysis yields estimates for the critical exponents in the low temperature phase.Comment: 19 pages 11 figures, ILL-(TH)-93-