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Stephen S. Leroy

Abstract

The effect of the diurnal cycle when monitoring the climate from low earth orbit is examined briefly. Equations are derived that relate the harmonics of the diurnal cycle to temporal sampling error and drift rates in that error. Special attention is given to nodal precession of satellite orbits. Using an insolated blackbody as a simple model for the diurnal cycle, roughly simulating subtropical desert surface temperature, the effects of orbital precession are examined numerically. From an initial configuration, wherein satellites are evenly spaced in nodal crossing time, minor differences in precession rates lead to biases proportional to the amplitude of the semidiurnal cycle and inversely to the square root of the number of satellites. Overall biases for a single mission can be dramatically reduced by flying in a formation wherein the satellites' orbits are evenly distributed in their equator-crossing times. To monitor surface temperature, it is suggested that at least six satellites be flown in formation and that their precession rates be controlled to well within 25 min. The tolerance for monitoring any other variable can be scaled according to the size of its semidiurnal cycle.

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Stephen S. Leroy

Abstract

A Bayesian approach to detecting forced climate signals in a dataset is presented. First, the detection algorithm derived is shown to be capable of uniquely identifying several signals optimally. Other detection techniques are shown to be limiting cases. Second, this approach naturally lends itself to rating models relatively according to their predictions. Both the accuracy of the model prediction and the precision of the prediction are accounted for in rating models. In general, complex models are less probable than simpler models. Finally, this approach to detection is used to detect a signal induced by the solar cycle in the surface temperature record over the past 100 yr. The solar cycle signal-to-noise ratio is found to be ∼1 but is probably not detected. Estimates of the natural variability noise are taken from model prescriptions, each of which is vastly different. The Geophysical Fluid Dynamics Laboratory models, though, best match the residual temperature fluctuations after the signals are subtracted. The Bayesian viewpoint emphasizes the need for the estimation of uncertainties associated with model predictions. Without estimates of uncertainties it is impossible to determine the predictive capabilities of models.

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Stephen S. Leroy

Abstract

Optimal fingerprinting is applied to estimate the amount of time it would take to detect warming by increased concentrations of carbon dioxide in monthly averages of temperature profiles over the Indian Ocean. A simple radiative–convective model is used to define the pattern of the warming signal, and the first 100 yr of the 1000-yr control run of the Geophysical Fluid Dynamics Laboratory atmospheric–oceanic global climate model is used to estimate the natural variability of the upper-air temperatures. The signal is assumed to be the difference in two epochs of data, each epoch consisting of 12 consecutive months of monthly average temperature profiles. When the variabilities of monthly averages are assumed independent of each other, the difference in August upper-air temperatures yields the strongest fingerprint, giving a time span for a one-sigma detection of 22 yr. When correlations of natural variability between months are considered, the one-sigma detection time is 10 yr. If only an annual average profile is used, the timescale for one-sigma detection increases to 14 yr. These timescales depend on subjective judgments of the details of the model-predicted pattern of global warming. In general, using upper-air temperatures adds approximately two independent pieces of information in detecting global warming for every surface-air temperature measurement, most likely due to the expected overall pattern of tropospheric warming–stratospheric cooling. Finally, testing climate models with data must be undertaken in order to understand the uncertainties in model-predicted global warming patterns and the predictive capability of models in general.

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Stephen S. Leroy
,
Gianluca Redaelli
, and
Barbara Grassi

Abstract

The prioritization accorded to observation types currently being considered for a space-based climate observing system is extended from a previous study. Hindcast averages and trends from 1970 through 2005 of longitude–latitude maps of 200-hPa geopotential height and of net downward shortwave and longwave radiation at the top of the atmosphere are investigated as relevant tests of climate models for predicting multidecadal surface air temperature change. To discover the strongest tests of climate models, Bayes’s theorem is applied to the output provided by phase 5 of the Coupled Model Intercomparison, and correlations of hindcasts and multidecadal climate prediction are used to rank the observation types and long-term averages versus long-term trends. Spatial patterns in data are shown to contain more information for improving climate prediction than do global averages of data, but no statistically significant test is found by considering select locations on the globe. Eigenmodes of intermodel differences in hindcasts may likely serve as tests of climate models that can improve interdecadal climate prediction, in particular the rate of Arctic tropospheric expansion, which is measurable by Earth radio occultation.

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Stephen S. Leroy
and
Andrew P. Ingersoll

Abstract

Radio scintillations in Pioneer Venus radio Occultation data are simulated assuming that the index of refraction fluctuations in Venus's atmosphere responsible for the scintillations are directly caused by gravity wave fluctuations. The gravity waves are created by a global convection layer between 50- and 55-km attitude in Venus's atmosphere and propagate vertically. The authors compare the simulated scintillations with data from Pioneer Venus.

These gravity waves can explain the spectral shape and amplitude of the radio scintilations. The shape at high frequencies is controlled by wave breaking, which yields a saturated spectrum. The amplitude is subject to parameters such as the intensity of the convection, the angle between the zonal winds and the beam path, and the zonal wind profile at polar latitudes. To match the observed amplitude of the scintillations, the velocity variations of the energy-bearing eddies in the convection must be at least 2 m s−1. This value is consistent with the Venus balloon results of Sagdeev et al. and is in the middle of the range considered by Leroy and Ingersoll in their study of convectively generated gravity waves. The later study, combined with the lower bound on velocity from the present study, then yields lower bounds on the vertical fluxes of momentum and energy in the Venus atmosphere.

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Stephen S. Leroy
and
Mark J. Rodwell

Highly accurate data can serve the numerical weather prediction, climate prediction, and atmospheric reanalysis communities by better enabling the diagnosis of model error through the careful examination of the diagnostics of data assimilation, especially the firstguess departures and the analysis increments. The highly accurate data require no bias correction for instrument error, leaving the possibility of confusion with error in forward models for observations as the lone hindrance to the diagnosis of model error. With this scenario in mind, we conducted numerical experiments to investigate the potential confusion using the data assimilation system at the European Centre for Medium-Range Weather Forecasts. We found that large-scale systematic model error can be misattributed to error in the forward models for observations, thereby reducing systematic firstguess departures and impeding the mitigation of model error. The same large-scale model error generated a 20% increase in analyzed specific humidity near the tropopause, suggesting that current observational data cannot constrain the upper tropospheric humidity in current models, which contributes substantially to greenhouse forcing of the climate. We expect that the confusion of model error for an error in the forward models for observations occurs regardless of the objective method used to diagnose model error.

Our findings underline the importance for continued improvement in radiative transfer calculations and highlight the value of multiple sources of accurate data that are redundant in their sensitivity to atmospheric variables yet orthogonal in their radiation physics.

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Stephen S. Leroy
and
James G. Anderson

Abstract

A complete accounting of model uncertainty in the optimal detection of climate signals requires normalization of the signals produced by climate models; however, there is not yet a well-defined rule for the normalization. This study seeks to discover such a rule. The authors find that, to arrive at the equations of optimal detection from a general application of Bayesian statistics to the problem of climate change, it is necessary to assume that 1) the prior probability density function (PDF) for climate change is separable into independent PDFs for sensitivity and the signals’ spatiotemporal patterns; 2) postfit residuals are due to internal variability and are normally distributed; 3) the prior PDF for sensitivity is uninformative; and 4) a continuum of climate models used to estimate model uncertainty gives a normally distributed PDF for the spatiotemporal patterns for the climate signals. This study also finds that the rule for normalization of the signals’ patterns is a simple division of model-simulated climate change in any observable quantity or set of quantities by a change in a single quantity of interest such as regionally averaged temperature or precipitation. With this normalization, optimal detection yields the most probable estimates of the underlying changes in the region of interest due to external forcings. Data outside the region of interest add information that effectively suppresses the interannual fluctuations associated with internal climate variability.

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Stephen S. Leroy
and
Andrew P. Ingersoll

Abstract

The emission of internal gravity waves from a layer of dry convection embedded within a stable atmosphere with static stability and zonal winds varying in height is calculated. This theory is applied to Venus to investigate whether these waves can help support the westward maximum of angular momentum of Venus's middle atmosphere. The emission mechanism is similar to that suggested for driving the gravity modes of the Sun and relates the amplitude and spectrum of the waves to the amplitude and spectrum of the convection. Waves are damped by several mechanisms: wavebreaking in the stable atmosphere, critical layer absorption, reabsorption by the convection, and wave radiation to space. The authors use plane parallel geometry without rotation and assume sinusoidal wave fluctuations in the horizontal dimensions. The vertical dependence is determined using the WKBJ approximation.

It is found that convectively generated gravity waves do not exert an acceleration where the westward winds are greatest. Instead, they deposit westward momentum in a 1-km thick layer just above the convection. Other waves deposit eastward momentum far above the westward wind maximum where decelerations can exceed 20 m s−1 day−1, comparable to deceleration amplitudes in Earth's mesosphere. Although the momentum fluxes by gravity waves are substantial, the vertical profile of acceleration does not match what is required for supporting Venus's atmospheric superrotation.

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Stephen S. Leroy
,
James G. Anderson
, and
George Ohring

Abstract

Long-term trends in the climate system are always partly obscured by naturally occurring interannual variability. All else being equal, the larger the natural variability, the less precisely one can estimate a trend in a time series of data. Measurement uncertainty, though, also obscures long-term trends. The way in which measurement uncertainty and natural interannual variability interact in inhibiting the detection of climate trends using simple linear regression is derived and the manner in which the interaction between the two can be used to formulate accuracy requirements for satellite climate benchmark missions is shown. It is found that measurement uncertainty increases detection times, but only when considered in direct proportion to natural variability. It is also found that detection times depend critically on the correlation time of natural variability and satellite lifetime. As a consequence, requirements on satellite climate benchmark accuracy and mission lifetime must be directly related to the natural variability of the climate system and its associated correlation times.

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Stephen S. Leroy
,
Chi O. Ao
, and
Olga Verkhoglyadova

Abstract

Bayesian interpolation for mapping GPS radio occultation data on a sphere is explored and its performance evaluated. Bayesian interpolation is ideally suited to the task of fitting data randomly and nonuniformly distributed with unknown error without overfitting the data. The geopotential height at dry pressure 200 hPa is simulated as data with theoretical distributions of the Challenging Mini-Satellite Payload (CHAMP) and of the Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC). The simulated CHAMP data are found to be best fit with a spherical harmonic basis of 14th degree; the COSMIC data with a spherical harmonic basis of 20th degree. The best regularizer mimics a spline fit, and relaxing the penalty for purely meridional structures or for the global mean yields little advantage. Climatologies are most accurately established by binning in ≃2-day intervals to best resolve synoptic structures in space and time. Finally, Bayesian interpolation is shown to negate a source of systematic sampling error obtained in binning and averaging highly nonuniform data but to incur another systematic error due to incomplete resolution of the background atmosphere, notably in the Southern Hemisphere.

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