An official website of the United States government
Abstract Geostationary weather satellites collect high‐resolution data comprising a series of images. The Derived Motion Winds (DMW) Algorithm is commonly used to process these data and estimate atmospheric winds by tracking features in the images. However, the wind estimates from the DMW Algorithm are often missing and do not come with uncertainty measures. Also, the DMW Algorithm estimates can only be half‐integers, since the algorithm requires the original and shifted data to be at the same locations, in order to calculate the displacement vector between them. This motivates us to statistically model wind motions as a spatial process drifting in time. Using a covariance function that depends on spatial and temporal lags and a drift parameter to capture the wind speed and wind direction, we estimate the parameters by local maximum likelihood. Our method allows us to compute standard errors of the local estimates, enabling spatial smoothing of the estimates using a Gaussian kernel weighted by the inverses of the estimated variances. We conduct extensive simulation studies to determine the situations where our method performs well. The proposed method is applied to the GOES‐15 brightness temperature data over Colorado and reduces prediction error of brightness temperature compared to the DMW Algorithm.
more »
« less
This content will become publicly available on July 1, 2026
The sharp lifespan for a system of multiple speed wave equations: Radial case
Ohta examined a system of multiple speed wave equations with small initial data and demonstrated a finite time blowup. We show, in the radial case, that the same system exists almost globally with the same lifespan as a lower bound. To do this, we use integrated local energy estimates, weighted local energy estimates, the Morawetz estimate that results from using the scaling vector field as a multiplier, and mixed-speed ghost weights.
more »
« less
- Award ID(s):
- 2054910
- PAR ID:
- 10611846
- Publisher / Repository:
- AIMS Press
- Date Published:
- Journal Name:
- Communications in Analysis and Mechanics
- Volume:
- 17
- Issue:
- 3
- ISSN:
- 2836-3310
- Page Range / eLocation ID:
- 662--682
- Subject(s) / Keyword(s):
- wave equations local energy estimates multiple speed almost global existence
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Smart Servers, Smarter Speed Scaling: A Decentralized Algorithm for Data Center Efficiency A team of researchers from Georgia Tech and the University of Minnesota has introduced a cutting-edge algorithm designed to optimize energy use in large-scale data centers. As detailed in their paper “Distributed Rate Scaling in Large-Scale Service Systems,” the team developed a decentralized method allowing each server to adjust its processing speed autonomously without the need for communication or knowledge of system-wide traffic. The algorithm uses idle time as a local signal to guide processing speed, ensuring that all servers converge toward a globally optimal performance rate. This innovation addresses a critical issue in modern computing infrastructure: balancing energy efficiency with performance under uncertainty and scale. The authors demonstrate that their approach not only stabilizes the system but achieves asymptotic optimality as the number of servers increases. The work is poised to significantly reduce energy consumption in data centers, which are projected to account for up to 8% of U.S. electricity use by 2030.more » « less
-
Abstract In this paper we study hybridized discontinuous Galerkin methods for viscoacoustic wave equations with a general number of viscosity terms. For viscoacoustic equations rewritten as a first order symmetric hyperbolic system, we develop a hybridized local discontinuous Galerkin method which is robust for the number of viscosity terms. We show that the method satisfies a discrete energy estimate such that the implicit constants in the energy estimate are independent of the number of viscosity terms and the length of simulation time. Furthermore, we show that the sizes of reduced system after static condensation are independent of the number of viscosity terms. Optimal a priori error estimates with the Crank–Nicolson scheme are proved and numerical test results are included.more » « less
-
The increasing penetration of renewable energy resources in distribution systems necessitates high-speed monitoring and control of voltage for ensuring reliable system operation. However, existing voltage control algorithms often make simplifying assumptions in their formulation, such as real-time availability of smart meter measurements (for monitoring), or real-time knowledge of every power injection information (for control). This paper leverages the recent advances made in high-speed state estimation for real-time unobservable distribution systems to formulate a deep reinforcement learning (DRL)-based control algorithm that utilizes the state estimates alone to control the voltage of the entire system. The results obtained for a modified (renewable-rich) IEEE 34-node distribution feeder indicate that the proposed approach excels in monitoring and controlling voltage of active distribution systems.more » « less
-
Abstract We provide a complete local well-posedness theory inHsbased Sobolev spaces for the free boundary incompressible Euler equations with zero surface tension on a connected fluid domain. Our well-posedness theory includes: (i) Local well-posedness in the Hadamard sense, i.e., local existence, uniqueness, and the first proof of continuous dependence on the data, all in low regularity Sobolev spaces; (ii) Enhanced uniqueness: Our uniqueness result holds at the level of the Lipschitz norm of the velocity and the$$C^{1,\frac{1}{2}}$$regularity of the free surface; (iii) Stability bounds: We construct a nonlinear functional which measures, in a suitable sense, the distance between two solutions (even when defined on different domains) and we show that this distance is propagated by the flow; (iv) Energy estimates: We prove refined, essentially scale invariant energy estimates for solutions, relying on a newly constructed family of elliptic estimates; (v) Continuation criterion: We give the first proof of a sharp continuation criterion in the physically relevant pointwise norms, at the level of scaling. In essence, we show that solutions can be continued as long as the velocity is in$$L_T^1W^{1,\infty}$$and the free surface is in$$L_T^1C^{1,\frac{1}{2}}$$, which is at the same level as the Beale-Kato-Majda criterion for the boundaryless case; (vi) A novel proof of the construction of regular solutions. Our entire approach is in the Eulerian framework and can be adapted to work in more general fluid domains.more » « less
