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DOE OSTI2024

When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling

Recent advances in differentiable modeling, a genre of physics-informed machine learning that trains neural networks (NNs) together with process-based equations, have shown promise in enhancing hydrological models' accuracy, interpretability, and knowledge-discovery potential. Current differentiable models are efficient for NN-based parameter regionalization, but the simple explicit numerical schemes paired with sequential calculations (operator splitting) can incur numerical errors whose impacts on models' representation power and learned parameters are not clear. Implicit schemes, however, cannot rely on automatic differentiation to calculate gradients due to potential issues of gradient vanishing and memory demand. Here we propose a “discretize-then-optimize” adjoint method to enable differentiable implicit numerical schemes for the first time for large-scale hydrological modeling. The adjoint model demonstrates comprehensively improved performance, with Kling–Gupta efficiency coefficients, peak-flow and low-flow metrics, and evapotranspiration that moderately surpass the already-competitive explicit model. Therefore, the previous sequential-calculation approach had a detrimental impact on the model's ability to represent hydrological dynamics. Furthermore, with a structural update that describes capillary rise, the adjoint model can better describe baseflow in arid regions and also produce low flows that outperform even pure machine learning methods such as long short-term memory networks. The adjoint model rectified some parameter distortions but did not alter spatial parameter distributions, demonstrating the robustness of regionalized parameterization. Despite higher computational expenses and modest improvements, the adjoint model's success removes the barrier for complex implicit schemes to enrich differentiable modeling in hydrology.

58 GEOSCIENCES↗

DOE OSTI2026

3D TRISO particle-explicit compact meshing

The TRI-structural ISOtropic (TRISO) layered fuel particle is a robust nuclear fuel form offering enhanced safety and performance for advanced reactor concepts, including high-temperature gas-cooled reactors and other Generation IV designs. These poppy-seed-sized particles are embedded in a graphite matrix to form fuel elements that must withstand elevated temperatures and high burn-up levels. The heterogeneous nature of these fuel elements — comprising thousands of randomly distributed TRISO particles — produces complex stress fields and thermal gradients that one- and two-dimensional models cannot accurately capture. While three-dimensional modeling has improved predictions of dimensional changes, internal pressure buildup, and fission product transport under irradiation, current approaches rely on homogenized material properties that are known to have considerable divergence from experimental observations. This work presents a methodology for optimized random packing of TRISO fuel compacts and full three-dimensional mesh generation within the BISON fuel performance code, with each particle coating layer individually discretized. The resulting mesh was demonstrated through heat conduction simulations under representative in-reactor operating conditions, showing strong agreement with expected behavior. This capability enables detailed analysis of particle-to-particle interactions, matrix cracking mechanisms, and the statistical distribution of coating layer failures — all of which directly govern fuel performance and safety margins.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Innovating the next generation of commercial smart building software

Nearly 30% of commercial building energy use is wasted due to equipment faults and HVAC controls problems. The result is increased emissions, compromised comfort and productivity, and less reliable coordination of building power needs with a clean grid. The energy impact alone represents $17 billion in potential savings. Today’s smart building software provides a robust solution to address these operational deficiencies. Energy management and information systems (EMIS) are saving up to 9% on average, with two-year paybacks. They are being incorporated into energy management processes, commissioning services, and utility programs. As effective as they are, two barriers prevent even deeper benefits; limited personnel to fix problems once they are identified, and the expense and time to manually implement changes in control systems. In partnership with the research community, the EMIS industry is developing new capabilities to overcome these barriers. Moving beyond siloed products for either fault detection and diagnostics, or optimal control, these new capabilities empower users to not only automatically identify faults, but also to push corrective action, and control improvements to their buildings. In this paper, several areas for enhancements are documented: ‘one-time’ correction of faults such as setpoints, schedules, and economizer lockouts; short-term active testing for automated proportional integral derivative (PID) loop tuning and functional testing; and continuous supervisory control for demand flexibility and year-round efficiency. Results are presented from a pair of partner implementations out of a dozen providers integrating these enhancements into their products, including field tests from across the country, and insights into operator acceptance and integration into operations and maintenance practices.

Casillas, Armando↗

NASA NTRS2006

Diffusion Bonding of Silicon Carbide Ceramics using Titanium Interlayers

Robust joining approaches for silicon carbide ceramics are critically needed to fabricate leak free joints with high temperature mechanical capability. In this study, titanium foils and physical vapor deposited (PVD) titanium coatings were used to form diffusion bonds between SiC ceramics using hot pressing. Silicon carbide substrate materials used for bonding include sintered SiC and two types of CVD SiC. Microscopy results show the formation of well adhered diffusion bonds. The bond strengths as determined from pull tests are on the order of several ksi, which is much higher than required for a proposed application. Microprobe results show the distribution of silicon, carbon, titanium, and other minor elements across the diffusion bond. Compositions of several phases formed in the joint region were identified. Potential issues of material compatibility and optimal bond formation will also be discussed.

Halbig, Michael C.↗

NASA NTRS2004

Application of Simulated Annealing and Related Algorithms to TWTA Design

Simulated Annealing (SA) is a stochastic optimization algorithm used to search for global minima in complex design surfaces where exhaustive searches are not computationally feasible. The algorithm is derived by simulating the annealing process, whereby a solid is heated to a liquid state and then cooled slowly to reach thermodynamic equilibrium at each temperature. The idea is that atoms in the solid continually bond and re-bond at various quantum energy levels, and with sufficient cooling time they will rearrange at the minimum energy state to form a perfect crystal. The distribution of energy levels is given by the Boltzmann distribution: as temperature drops, the probability of the presence of high-energy bonds decreases. In searching for an optimal design, local minima and discontinuities are often present in a design surface. SA presents a distinct advantage over other optimization algorithms in its ability to escape from these local minima. Just as high-energy atomic configurations are visited in the actual annealing process in order to eventually reach the minimum energy state, in SA highly non-optimal configurations are visited in order to find otherwise inaccessible global minima. The SA algorithm produces a Markov chain of points in the design space at each temperature, with a monotonically decreasing temperature. A random point is started upon, and the objective function is evaluated at that point. A stochastic perturbation is then made to the parameters of the point to arrive at a proposed new point in the design space, at which the objection function is evaluated as well. If the change in objective function values (Delta)E is negative, the proposed new point is accepted. If (Delta)E is positive, the proposed new point is accepted according to the Metropolis criterion: rho((Delta)f) = exp((-Delta)E/T), where T is the temperature for the current Markov chain. The process then repeats for the remainder of the Markov chain, after which the temperature is decremented and the process repeats. Eventually (and hopefully), a near-globally optimal solution is attained as T approaches zero. Several exciting variants of SA have recently emerged, including Discrete-State Simulated Annealing (DSSA) and Simulated Tempering (ST). The DSSA algorithm takes the thermodynamic analogy one step further by categorizing objective function evaluations into discrete states. In doing so, many of the case-specific problems associated with fine-tuning the SA algorithm can be avoided; for example, theoretical approximations for the initial and final temperature can be derived independently of the case. In this manner, DSSA provides a scheme that is more robust with respect to widely differing design surfaces. ST differs from SA in that the temperature T becomes an additional random variable in the optimization. The system is also kept in equilibrium as the temperature changes, as opposed to the system being driven out of equilibrium as temperature changes in SA. ST is designed to overcome obstacles in design surfaces where numerous local minima are separated by high barriers. These algorithms are incorporated into the optimal design of the traveling-wave tube amplifier (TWTA). The area under scrutiny is the collector, in which it would be ideal to use negative potential to decelerate the spent electron beam to zero kinetic energy just as it reaches the collector surface. In reality this is not plausible due to a number of physical limitations, including repulsion and differing levels of kinetic energy among individual electrons. Instead, the collector is designed with multiple stages depressed below ground potential. The design of this multiple-stage collector is the optimization problem of interest. One remaining problem in SA and DSSA is the difficulty in determining when equilibrium has been reached so that the current Markov chain can be terminated. It has been suggested in recent literature that simulating the thermodynamic properties opecific heat, entropy, and internal energy from the Boltzmann distribution can provide good indicators of having reached equilibrium at a certain temperature. These properties are tested for their efficacy and implemented in SA and DSSA code with respect to TWTA collector optimization.

Radke, Eric M.↗

DOE OSTI2024

Mechanically activated and deactivated ion transport across nanopores with heterogeneous surface charge distributions

To mimic the intricate and adaptive functionalities of biological ion channels, electrohydrodynamic ion transport has been studied extensively, albeit mostly, across uniformly charged nanochannels. Here, we analyze the ion transport under coupled electric field and pressure across heterogeneously charged nanopores with oppositely charged sections on their lateral surface. We only consider such pores with symmetric hourglass-like and cylindrical shapes to focus on the effects of the non-uniform surface charge distribution. Finite-element simulations of a continuum model demonstrate that a pressure applied in either direction of the pore-axis equally suppresses or amplifies the ionic conductance, depending on the electric field polarity, by distorting the quasi-static distribution of ions in the pore. The resulting anomalous mechanical deactivation and activation of ionic current under opposite voltage biases exhibit the functional modularity of our setup, while their intensities are highly tunable, substantially greater than those of analogous behaviors in other nanochannels, and fundamentally correlated to ionic current rectification (ICR) in our pores. A detailed study of ICR subsequently reveals its counterintuitive non-monotonous variations, in the pores, with the magnitude of applied voltage and the pore length, that can help optimize their diode-like behavior. We further illustrate that while the hourglass-shaped nanopores yield the more efficient mechanical suppressors of ion transport, their cylindrical analogs are the superior rectifiers and mechanical amplifiers of ion conduction. Therefore, this article provides a blueprint for the strategic design of nanofluidic circuits to attain a robust, modular, and tunable control of ion transport under external electrical and mechanical stimuli.

Physics↗

DOE OSTI2025

Dynamical Sketching for Enhanced Communication Efficiency in Federated Learning

Federated learning (FL) has revolutionized distributed machine learning by enabling collaborative model training without sharing local data. However, communication efficiency and privacy guarantees remain significant challenges. This paper introduces a dynamic sketching mechanism in FL, optimizing the trade-off between communication efficiency and model accuracy. By dynamically selecting the sketch matrix size, our approach adapts to the evolving characteristics of the data and the model, ensuring optimal performance across diverse scenarios. We leverage Bayesian optimization to systematically tune the sketch parameters, achieving an effective balance between resource efficiency and model performance. Experimental results on the MNIST dataset using a convolutional neural network (CNN) architecture validate the proposed method's efficiency and scalability. Our dynamic sketching approach significantly outperforms fixed-size sketching techniques, achieving higher compression ratios (up to 62x) and providing better privacy guarantees while maintaining high model accuracy. These findings highlight the robustness and versatility of our approach and make it a valuable solution for privacy-preserving, communication-efficient federated learning.

Afrose, Sharmin [ORNL]↗

NASA NTRS2016

Design of an Electric Propulsion System for SCEPTOR

The rise of electric propulsion systems has pushed aircraft designers towards new and potentially transformative concepts. As part of this effort, NASA is leading the SCEPTOR program which aims at designing a fully electric distributed propulsion general aviation aircraft. This article highlights critical aspects of the design of SCEPTOR's propulsion system conceived at Joby Aviation in partnership with NASA, including motor electromagnetic design and optimization as well as cooling system integration. The motor is designed with a finite element based multi-objective optimization approach. This provides insight into important design tradeoffs such as mass versus efficiency, and enables a detailed quantitative comparison between different motor topologies. Secondly, a complete design and Computational Fluid Dynamics analysis of the air breathing cooling system is presented. The cooling system is fully integrated into the nacelle, contains little to no moving parts and only incurs a small drag penalty. Several concepts are considered and compared over a range of operating conditions. The study presents trade-offs between various parameters such as cooling efficiency, drag, mechanical simplicity and robustness.

SCEPTOR↗

NASA NTRSDate not supplied

Summary of the virtual Space Radiation “2022 Biospecimen and Tissue Sharing Summit.”

The Space Radiation Element (SRE) of the Human Research Program (HRP) aims to establish a robust biospecimen and tissue sharing collection (BTSC) to improve sample collection, tracking, access, distribution, and usability to maximize scientific return with intention. Leveraging biospecimens and tissues from prior experiments helps HRP achieve its scientific goals to characterize and mitigate the human health impacts of spaceflight by maximizing resources. The project intends to expand on the National Aeronautics and Space Agency’s (NASA) current resources and institutional knowledge to provide ongoing modernization to improve the usability and access to the current biospecimen archive. SRE organized and held a three-day virtual workshop September 13-15, 2022, to engage with the research community with the following goals: - Share information about: - Space Radiation’s current Biospecimen and Tissue Sharing Project; - Software implementation to track biospecimens; - NASA’s current tissue sharing capabilities and projects; and - Collect community feedback on how to develop, streamline, and optimize accessible and usable processes. The first two days featured speakers internal and external to NASA who presented on current resources, best practices, lessons learned, and researcher perspectives. On the third day, a set of key questions were presented, and participants were invited to discuss and provide input.

Shelita Hall Augustus↗

DOE OSTI2025

Game Theory Approaches for System-level Incentive Design

This report presents a generalized Stackelberg game framework for designing and evaluating financial incentives that enhance power system resilience through strategic deployment of distributed energy resources(DERs) under various contingencies. The proposed approach addresses the challenge of coordinating individual community investment decisions to meet system-wide resilience objectives. The framework is demonstrated in a three-community test system subjected to two transmission contingency scenarios: inter-community line failure (Case 1) and complete main grid disconnection (Case 2). In both cases, three incentive levels are compared: a Base case with no financial incentives, and low and high incentive cases. In Case 1, the Base case (no incentives) results in a total installed DER capacity of 217.2 MW, with no load shedding due to alternative routing, but community costs remain high. Increasing incentives raises DER deployment to 286.9 MW, lowers aggregate community costs by $22M annually, and completely avoids the need for costly new transmission line construction. In Case 2, the Base case results in 24.3 MWh of unserved load; introducing incentives eliminates all load shedding and ensures up to 89 MWh of battery storage is available for emergency reserve. These results demonstrate that targeted incentives can dramatically improve grid resilience and cost-effectiveness. The framework thus offers policymakers and system planners a robust tool to quantify and compare the effectiveness of incentive programs for multi-community transmission networks behavior, system resilience, and economic efficiency.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2026

Quantifying Membrane Structure and Dynamics during Bioproduct Production in Zymomonas mobilis by Molecular Simulation

The conversion of lignocellulosic biomass into biofuels and bioproducts by microbial biorefineries is central to a sustainable chemical industry. Zymomonas mobilis is one such biorefinery chassis and is resistant to ethanol stress, leading to its use in biomass conversion to biofuels and bioproducts. However, Z. mobilis growth is often inhibited by organic acids, aldehydes, alcohols, ketones, and amides found in biomass hydrolysate. The resulting slow growth inhibits production and as a result drives up the price for the resulting products. One hypothesis is that these molecules interact with or disrupt the bacterial membrane, triggering stress responses and hindering growth. To test this hypothesis at the molecular level, we employ all-atom molecular dynamics (MD) simulations to investigate lignocellulose-derived small molecules and their impact on a biologically relevant Z. mobilis membrane model. Simulations were conducted across a range of inhibitor concentrations from 0 to 2.5 mol %, analyzing key membrane properties such as area per lipid (APL), membrane thickness, lipid-order parameter (−S CH ), lateral diffusion coefficient (D xy ), and permeability coefficient (Pm). From simulation, we observed altered membrane structure and dynamics at these modest small molecule concentrations commonly found in hydrolysates. Generally, the membranes become thinner, with a higher area per lipid and lower-order parameter as the small molecule concentration increases. These trends are stronger for more hydrophobic molecules with greater hydrophobic bulk, as isobutanol, propanol, and propanoic acid showed greater membrane perturbations as the concentration increased compared to other small molecules. Tracking small molecule distributions directly in our equilibrium simulations allows us to determine concentration-dependent free energy profiles for these molecules. While the trends are noisy, generally the barriers to crossing the membrane decrease as the concentration increases, indicating that the membranes become leakier as small molecule concentrations rise. Comparing between native Z. mobilis membranes with hopanoids and membranes sharing the same phospholipid composition but without hopanoids, hopanoids stabilize and order the membrane for smaller molecules to maintain membrane structure but appear insufficient for larger hydrophobic molecules like isobutanol. These findings provide a mechanistic understanding of how small molecules found in biomass degradation streams interact with the Z. mobilis membrane, offering valuable insights for future strain engineering efforts to optimize biofuel and bioproduct synthesis from biomass feedstocks by highlighting limits to small molecule tolerance. This knowledge can guide the modification of membrane composition to develop more robust microbes, thereby improving microbial survival and yields in industrial contexts.

Singh, Nitin Kumar [Michigan State Univ., East Lan↗

DOE OSTI2025

Strategic Placement and Sizing of Distributed Generation for Resilience Enhancement of Distribution Grids With Microgrid Formation

The rise in frequency and severity of extreme weather events highlights the need for resilient power distribution networks. Microgrids can help improve the resilience of distribution grids by providing continuous power supply using local distribution generation (DG) when the distribution grid fails. In this paper, we propose an approach for optimal placement and sizing of DG to form multiple microgrids throughout the distribution network by restoration actions such as switching operations in case of distribution grid outages caused by extreme weather events. Considering the randomness of damaged distribution lines, the DG placement and sizing problem is formulated as a two-stage stochastic mixed-integer program, with the first stage determining the placement and size of DG, and the second stage focusing on minimizing the amount of load shedding through network restoration and microgrid formations for each scenario. Due to the large number of scenarios, the sample average approximation (SAA) method is employed to solve the problem. The results of case studies on a modified IEEE 33 bus distribution grid demonstrate the effectiveness of the proposed DG placement and sizing strategy in improving the resilience of distribution grids by allowing the formation of multiple microgrids. In addition, the robustness and accuracy of the SAA method are validated through various case studies.

Distributed generation planning↗

DOE OSTI2025

Graph-Learning-Assisted State and Event Tracking for Solar-Penetrated Power Grids with Heterogeneous Data Sources

Unlike transmission systems, distribution systems do not typically contain sufficient metering to enable real-time state estimation. The lack of sufficient real-time measurements prohibits accurate and timely monitoring of the state of distribution systems. As a result, control and optimal operation of distribution systems, especially those containing large numbers of renewable generation units are not possible without proper data and information about the current state of the system. The main motivation of this project is to address this shortcoming by developing an approach which provides “predicted” real-time measurements so that they can be used to execute a distribution system state estimator. Thus, the objective of the project is to make the distribution systems fully observable, such that the hosting capacity for solar generation can be accurately estimated, and unnecessary solar curtailments can be avoided. In order to accomplish this goal, the project investigated the use of a grid-model-informed machine learning (ML) tool which integrates heterogeneous data streams obtained from AMI meters, SCADA as well as PMU measurements and created synchronous measurement snapshots for the state estimator (SE); and developed a hybrid robust SE which provides not only accurate state estimates but also real-time feedback for the ML model refinement.

14 SOLAR ENERGY↗

DOE OSTI2025

Enhancement of PyARC for Westinghouse Electric Company’s Lead Fast Reactor Design and Modeling (Final TCF Report)

Westinghouse Electric Company is a nuclear reactor vendor headquartered in the U.S. that is developing advanced reactor technology for the U.S. and global markets. Westinghouse has been relying on the neutronics Argonne Reactor Codes (ARC) executed through the NEAMS Workbench and its PyARC module that are developed under the DOE-NE Nuclear Energy Advanced Modeling and Simulation (NEAMS) and Advanced Reactor Technology (ART) – Fast Reactor programs. Through this user experience, Westinghouse identified several enhancements that would benefit the ARC codes’ usability by the US industry and therefore its commercialization potential. The enhancements were proposed to deliver both improvements in workflow and analysis capabilities to better support effective fast reactor core design and analysis to the nuclear industry. The PyARC workflow was extended in this project by integrating non-neutronic ARC codes DASSH and NUBOW-3D. The Ducted Assembly Steady-State Heat equation (DASSH) code is developed at ANL to perform steady-state thermal hydraulic sub-channel analysis in liquid metal fast reactor assemblies to determine optimized coolant flow and temperature distributions, which in this project was updated and validated for lead fast reactor (LFR) applications. The interface between REBUS and NUBOW-3D were improved in this project to assess the impact of the core restraint design and thermal induced expansion effects on the reactivity of the core, and to model the deformations of the fuel assemblies induced by temperature and irradiation. Finally, the ARC models that were extensively verified and validated through various SFR-based modeling benchmarks are extended in this project through code-to-code comparison on relevant LFR-specific neutronics benchmarks against Monte-Carlo neutronic solutions. Overall, this work enables verification of the capability of the ARC codes for a wide range of Generation-IV reactor designs. The outcome of this project is the release of a comprehensive modeling toolkit of validated, robust and efficient codes, as well as their user interface, that enables industry to perform a wide range of fast reactor analyses for design and licensing of their concepts.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS2014

Robust Modal Filtering and Control of the X-56A Model with Simulated Fiber Optic Sensor Failures

The X-56A aircraft is a remotely-piloted aircraft with flutter modes intentionally designed into the flight envelope. The X-56A program must demonstrate flight control while suppressing all unstable modes. A previous X-56A model study demonstrated a distributed-sensing-based active shape and active flutter suppression controller. The controller relies on an estimator which is sensitive to bias. This estimator is improved herein, and a real-time robust estimator is derived and demonstrated on 1530 fiber optic sensors. It is shown in simulation that the estimator can simultaneously reject 230 worst-case fiber optic sensor failures automatically. These sensor failures include locations with high leverage (or importance). To reduce the impact of leverage outliers, concentration based on a Mahalanobis trim criterion is introduced. A redescending M-estimator with Tukey bisquare weights is used to improve location and dispersion estimates within each concentration step in the presence of asymmetry (or leverage). A dynamic simulation is used to compare the concentrated robust estimator to a state-of-the-art real-time robust multivariate estimator. The estimators support a previously-derived mu-optimal shape controller. It is found that during the failure scenario, the concentrated modal estimator keeps the system stable.

Modal Filtering↗

NASA NTRS2016

Robust Modal Filtering and Control of the X-56A Model with Simulated Fiber Optic Sensor Failures

Modal Filtering↗

DOE OSTI2025

Uncertainty quantification of a physics-informed model based on sparse identification of a Thermal Energy Distribution System

Integrated energy systems (IES)s are crucial for enhancing the economy and efficiency of power generation sources (e.g., nuclear energy) necessary to unleash American energy dominance. These systems can be integrated with thermal energy storage (TES) and intermittent renewable energies to optimize overall energy use, peak-load regulation, and demand-side responses. However, the stabilization of energy generation, transport, and utilization introduces operational complexities that exceed the challenges of managing each sub-component individually. Currently, though IESs rely on human operators for efficiency and stability, reducing human error risk and enhancing performance through automation is highly desirable. Recent advances at Idaho National Laboratory have demonstrated successful control of the Thermal Energy Distributed System (TEDS). However, the automatic control system depends on a deterministic Sparse Identification of Nonlinear Dynamics with Control (SINDyC) model, which are trained based on simulation data from physics-based simulations. Because of uncertainties in physics-based simulation, SINDyC model results in large discrepancies against experimental data and cannot be reliably used in automatic control. In this paper, we present an innovative approach to address these discrepancies by quantifying uncertainties and developing a more robust model. We first generated trajectories by using first-principles physics codes to encapsulate the experiment. Next, we trained thousands of models by randomly sampling these trajectories. We then collapsed all those models into one probabilistic SINDyC by fitting a multivariate Gaussian distribution onto the resulting coefficient’s distribution. Despite its simplicity, our approach successfully produced 95% confidence intervals that captured the experimental trajectories. It even did so with a higher probability and better U-pooling score across six of the seven relevant quantities of interest (QoIs), as compared to other classical approaches. In conclusion, ongoing research is focusing on generating new experimental trajectories to validate this approach, and on employing Bayesian calibration to refine parametric uncertainties and guide future model development efforts.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1999

Remote Sensing of Rain

The first problem addressed concerns passive-microwave rain retrievals. Most current approaches start by building off-line a cloud-model-derived database. Given data, the retrieval algorithms search the database for the microwave temperatures "closest" to the observed data, then after some fine-tuning (performed in different ways by different implementations) the rain is estimated to be that which corresponds to the selected (and fine-tuned) set of database temperatures. These approaches have three drawbacks: they cannot properly take into account the ambiguities which arise from the fact that several rain scenarios can produce the same observed temperatures; they are quite inefficient since they require manipulating a large database along with often complex "fine-tuning" procedures; and they cannot refine their estimates if additional data is available. This past year we have derived closed formulae relating observed microwave brightness temperatures, T(sub b), and the underlying rain rates, R: average T(sub b) =f (rain) and average rain = g (T(sub b)), along with the corresponding covariance matrices. These results are sufficient to describe the conditional probabilities p(R/T(sub b)) and p(T(sub b)/R) to second order. Progress has also been made towards deriving a robust description of the rain drop size distribution (DSD). The widespread approach consisting in parameterizing the DSD as a gamma-distribution in terms of the drop diameter D suffers from the facts that, in reality, the DSD is not a smooth function of D and that the largely arbitrary Gamma model imposes unintended behavior, which has implications on any quantities derived from the DSD model. We have therefore developed a non-parametric yet practical description of the DSD, which is particularly well-suited for use in remote-sensing applications. The diagram on the left shows a comparison between an actual DSD sample and the truncated non-parametric representation. One figure shows the relation between radar reflectivity and rain rate derived using this representation. Validation of the Tropical Rainfall Measuring Mission (TRMM) radar-radiometer combined R and DSD algorithm is underway. This algorithm was designed to make optimal use of the instantaneous reflectivity profiles measured by the TRMM radar and the microwave brightness temperatures measured by the TRMM passive radiometer. So far, it appears to be the most reliable TRMM rain algorithm.

Haddad, Ziad S.↗