An official website of the United States government
The rescaling of rainfall requires measurements of rainfall rates over many dimensions. This paper develops one approach using 10 m vertical spatial observations of the Doppler spectra of falling rain every 10 s over intervals varying from 15 up to 41 min in two different locations and in two different years using two different micro-rain radars (MRR). The transformation of the temporal domain into spatial observations uses the Taylor “frozen” turbulence hypothesis to estimate an average advection speed over an entire observation interval. Thus, when no other advection estimates are possible, this paper offers a new approach for estimating the appropriate frozen turbulence advection speed by minimizing power spectral differences between the ensemble of purely spatial radial power spectra observed at all times in the vertical and those using the ensemble of temporal spectra at all heights to yield statistically reliable scaling relations. Thus, it is likely that MRR and other vertically pointing Doppler radars may often help to obviate the need for expensive and immobile large networks of instruments in order to determine such scaling relations but not the need of those radars for surveillance.
more »
« less
On Observations of Correlation Functions and Power Spectra in Rain: Obfuscation by Advection and Sampling
Rain is often characterized using statistical approaches. Among the most common are temporal correlations and power (variance) spectra from time series measurements at a single location. Likewise, temporal observations over a network are used to deduce a radial distribution function and spatial power spectra. Often the spatial and temporal structures are treated as independent of each other. This assumption is no longer valid when the rain moves horizontally. Moreover, observations involve filtering of the data. In time, this may involve sampling over a sufficiently long period so as to increase statistical confidence in the measurement. The same is also true for spatial observations over a network which must contain a sufficient number of instruments for a reliable characterization of the spatial variability. This also usually includes some form of averaging over time as well. Temporal averaging amounts to a low pass filter that attenuates contributions from higher frequencies. In contrast, the finite dimension of a network acts as a high pass filter that tends to suppress the lower wavenumbers much larger than the dimension of the network. In this work the effects of both the advection of the rain and the observational filtering are considered for wide-sense statistically stationary and homogeneous rain along one-dimension for rain exponentially correlated in both space and time. It is found that advection and filtering can significantly shift the portrayal of the rain from the true structures. Consequently, rainfall characterizations from observations should not be over-generalized to other situations until the advection velocity is first taken into account using additional observations.
more »
« less
- Award ID(s):
- 1823072
- PAR ID:
- 10143442
- Date Published:
- Journal Name:
- 26th Conference on Probability and Statistics
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
In this paper, a distributed cooperative filtering strategy for state estimation has been developed for mobile sensor networks in a spatial–temporal varying field modeled by the advection–diffusion equation. Sensors are organized into distributed cells that resemble a mesh grid covering a spatial area, and estimation of the field value and gradient information at each cell center is obtained by running a constrained cooperative Kalman filter while incorporating the sensor measurements and information from neighboring cells. Within each cell, the finite volume method is applied to discretize and approximate the advection–diffusion equation. These approximations build the weakly coupled relationships between neighboring cells and define the constraints that the cooperative Kalman filters are subjected to. With the estimated information, a gradient-based formation control law has been developed that enables the sensor network to adjust formation size by utilizing the estimated gradient information. Convergence analysis has been conducted for both the distributed constrained cooperative Kalman filter and the formation control. Simulation results with a 9-cell 12-sensor network validate the proposed distributed filtering method and control law.more » « less
-
Abstract Predicting rain from large-scale environmental variables remains a challenging problem for climate models and it is unclear how well numerical methods can predict the true characteristics of rainfall without smaller (storm) scale information. This study explores the ability of three statistical and machine learning methods to predict 3-hourly rain occurrence and intensity at 0.5° resolution over the tropical Pacific Ocean using rain observations the Global Precipitation Measurement (GPM) satellite radar and large-scale environmental profiles of temperature and moisture from the MERRA-2 reanalysis. We also separated the rain into different types (deep convective, stratiform, and shallow convective) because of their varying kinematic and thermodynamic structures that might respond to the large-scale environment in different ways. Our expectation was that the popular machine learning methods (i.e., the neural network and random forest) would outperform a standard statistical method (a generalized linear model) because of their more flexible structures, especially in predicting the highly skewed distribution of rain rates for each rain type. However, none of the methods obviously distinguish themselves from one another and each method still has issues with predicting rain too often and not fully capturing the high end of the rain rate distributions, both of which are common problems in climate models. One implication of this study is that machine learning tools must be carefully assessed and are not necessarily applicable to solving all big data problems. Another implication is that traditional climate model approaches are not sufficient to predict extreme rain events and that other avenues need to be pursued.more » « less
-
This paper presents an inverse filtering procedure for developing estimates of "true" cone penetration tip re-sistance and sleeve friction values from measured cone penetration test data in interlayered soil profiles. Re-sults of prior studies of cone penetration in layered soil profiles are utilized for developing and evaluating the inverse filtering procedure. The inverse filtering procedure has three primary components: (1) a model for how the cone penetrometer acts as a low-pass spatial filter in sampling the true distribution of soil resistance versus depth, (2) a solution procedure for iteratively determining an estimate of the true cone penetration resistance profile from the measured profile given the cone penetration filter model, and (3) a procedure for identifying sharp transition interfaces and correcting the data at those interfaces. The details of the inverse filtering pro-cedure presented herein were developed with a focus on liquefaction problems, but the concepts and frame-work should be applicable to other problems. Example applications of the inverse filtering procedure are pre-sented for four CPT soundings illustrative of a range of soil profile characteristics. The proposed procedure provides an objective, repeatable, and automatable means for correcting cone penetration test data for thin-layer and transition zone effects.more » « less
-
It is important to understand the statistical–physical structure of the rain in the vertical so that observations aloft can be translated meaningfully into what will occur at the surface. In order to achieve this understanding, it is necessary to gather high temporal and spatial resolution observations of rain in the vertical. This can be achieved by translating radar Doppler spectra into drop size distributions. A long-standing difficulty in using such measurements, however, is the problem of vertical air motion, which can shift the Doppler spectra and therefore significantly alter the deduced drop size distributions and integrated variables. In this work, we overcome this difficulty by requiring that the measured radar reflectivity and the calculated rainfall rates satisfy fundamental physical theory. As a consequence, the mean vertical airspeed can be estimated and removed. Application of this new approach is demonstrated using vertically pointing Doppler radar observations in weak convection. It is shown that the new approach produces what appear to be better estimates of the rainfall rates as well as estimates of the temporal and spatial regionally coherent updraft and downdrafts occurring in the precipitation. The technique is readily applicable to other radars, especially those operating at non-attenuating frequencies.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
