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Many astrophysical analyses depend on estimates of redshifts (a proxy for distance) determined from photometric (i.e., imaging) data alone. Inaccurate estimates of photometric redshift uncertainties can result in large systematic errors. However, probability distribution outputs from many photometric redshift methods do not follow the frequentist definition of a Probability Density Function (PDF) for redshift — i.e., the fraction of times the true redshift falls between two limits z1 and z2 should be equal to the integral of the PDF between these limits. Previous works have used the global distribution of Probability Integral Transform (PIT) values to re-calibrate PDFs, but offsetting inaccuracies in different regions of feature space can conspire to limit the efficacy of the method. We leverage a recently developed regression technique that characterizes the local PIT distribution at any location in feature space to perform a local re-calibration of photometric redshift PDFs resulting in calibrated predictive distributions. Though we focus on an example from astrophysics, our method can produce predictive distributions which are calibrated at all locations in feature space for any use case.
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Metrics for Evaluating CMIP6 Representation of Daily Precipitation Probability Distributions
Abstract The performance of GCMs in simulating daily precipitation probability distributions is investigated by comparing 35 CMIP6 models against observational datasets (TRMM-3B42 and GPCP). In these observational datasets, PDFs on wet days follow a power-law range for low and moderate intensities below a characteristic precipitation cutoff scale. Beyond the cutoff scale, the probability drops much faster, hence controlling the size of extremes in a given climate. In the satellite products analyzed, PDFs have no interior peak. Contributions to the first and second moments tend to be single-peaked, implying a single dominant precipitation scale; the relationship to the cutoff scale and log-precipitation coordinate and normalization of frequency density are outlined. Key metrics investigated include the fraction of wet days, PDF power-law exponent, cutoff scale, shape of probability distributions, and number of probability peaks. The simulated power-law exponent and cutoff scale generally fall within observational bounds, although these bounds are large; GPCP systematically displays a smaller exponent and cutoff scale than TRMM-3B42. Most models simulate a more complex PDF shape than these observational datasets, with both PDFs and contributions exhibiting additional peaks in many regions. In most of these instances, one peak can be attributed to large-scale precipitation and the other to convective precipitation. Similar to previous CMIP phases, most models also rain too often and too lightly. These differences in wet-day fraction and PDF shape occur primarily over oceans and may relate to deterministic scales in precipitation parameterizations. It is argued that stochastic parameterizations may contribute to simplifying simulated distributions.
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- Award ID(s):
- 1936810
- PAR ID:
- 10433753
- Date Published:
- Journal Name:
- Journal of Climate
- Volume:
- 35
- Issue:
- 17
- ISSN:
- 0894-8755
- Page Range / eLocation ID:
- 5719 to 5743
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1175/JCLI-D-21-0617.1
