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Stephen D. Eckermann
,
Jun Ma
, and
Dave Broutman

Abstract

Numerical transform solutions for hydrostatic gravity waves generated by both uniform and sheared flow over elliptical obstacles are used to quantify effects of horizontal geometrical spreading on amplitude evolution with height. Both vertical displacement and steepness amplitudes are considered because of their close connections to drag parameterizations in weather and climate models. Novel diagnostics quantify the location and value of the largest wavefield amplitudes most likely to break at each altitude. These horizontal locations do not stray far from the obstacle peak even at high altitudes. Resulting vertical profiles of wave amplitude are normalized to remove density and refraction effects, thereby quantifying the horizontal geometrical spreading contribution, currently absent from parameterizations. Horizontal geometrical spreading produces monotonic amplitude decreases with height through wave-action conservation as waves propagate into progressively larger horizontal areas. Accumulated amplitude reductions are appreciable for all but the most quasi-two-dimensional obstacles with long axes orthogonal to the flow, and even these are impacted appreciably if the obstacle is rotated by more than 20°–30°. Profiles are insensitive to the obstacle’s functional form but vary strongly in response to changes in its horizontal aspect ratio. Responses to background winds are captured by a vertical coordinate transformation that remaps profiles to a universal form for a given obstacle. These results show that horizontal geometrical spreading has comparable or larger effects on wave amplitudes as the refraction of vertical wavenumbers and thus is important for accurate parameterizations of wave breaking and drag.

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Jun Yang
,
Weitao Lu
,
Ying Ma
, and
Wen Yao

Abstract

Cloud detection is a basic research for achieving cloud-cover state and other cloud characteristics. Because of the influence of sunlight, the brightness of sky background on the ground-based cloud image is usually nonuniform, which increases the difficulty for cirrus cloud detection, and few detection methods perform well for thin cirrus clouds. This paper presents an effective background estimation method to eliminate the influence of variable illumination conditions and proposes a background subtraction adaptive threshold method (BSAT) to detect cirrus clouds in visible images for the small field of view and mixed clear–cloud scenes. The BSAT algorithm consists of red-to-blue band operation, background subtraction, adaptive threshold selection, and binarization. The experimental results show that the BSAT algorithm is robust for all types of cirrus clouds, and the quantitative evaluation results demonstrate that the BSAT algorithm outperforms the fixed threshold (FT) and adaptive threshold (AT) methods in cirrus cloud detection.

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Jun Zhang
,
Jiming Sun
,
Wei Deng
, and
Yuxia Ma

Abstract

Double-moment schemes cannot accurately describe the evolution of the cloud droplet spectrum during condensation. Hence, a new triple-moment condensation scheme is developed to describe the evolution of cloud droplet spectra. In this scheme, a three-parameter gamma distribution function of the cloud droplet mass is adopted, and the prognostic equations of the spectral shape parameter and slope parameter are derived by means of the number concentration, cloud water content, and reflectivity factor of cloud droplets. The new parameterization scheme is compared with high-resolution Lagrangian and Eulerian bin schemes, double-moment schemes, and existing triple-moment schemes by performing simulations under different supersaturation values. The new scheme can reduce the cloud spectral error in the cloud water content and reflectivity factor caused by the fixed shape parameter in some bulk schemes. The spectra simulated with the new scheme match the Lagrangian analytical solutions well, with errors within approximately 1% in the cloud water content and reflectivity factor. The effects of curvature and solution on condensation growth are also tested using the new scheme, and a method of using multiple gamma distribution functions to characterize the multimodal spectrum of cloud droplets is proposed in the new condensation scheme. Ultimately, the formation of rain embryos from giant aerosols can be simulated via the new scheme.

Free access
Ge Chen
,
Jun Ma
,
Chaoyang Fang
, and
Yong Han

Abstract

A detailed study on global oceanic precipitation is carried out using the simultaneous TOPEX and TMR (TOPEX Microwave Radiometer) data. It is motivated by the success of a series of feasibility studies based on a few years of TOPEX–TMR data, and the availability of a decade-long new dataset that spans 1992–2002. In this context, a previously proposed rain probability index is improved by taking into account the difference of the dynamic range of the TOPEX-measured backscatter coefficients at the Ku and C bands and the latitudinally complementary sensitivities of the TOPEX and TMR rain detections, leading to a refined joint precipitation index, which is generally consistent and quantitatively comparable with existing precipitation climatologies from the Global Precipitation Climatology Project (GPCP) and the Comprehensive Ocean–Atmosphere Data Set (COADS). The new TOPEX–TMR precipitation climatology, on the one hand, confirms the fundamental features of global oceanic rainfall with additional details, and, on the other hand, reveals a number of interesting characteristics that are previously unknown or poorly defined. 1) The spatial variability of the western Pacific “rain pool” (the atmospheric counterpart of the oceanic warm pool) is characterized by an interannual zonal migration, an annual cycle of meridional seesaw, and a semiannual cycle of expansion and shrinking. 2) The Pacific, Atlantic, and Indian Ocean intertropical convergence zones (ITCZs) all have an annual cycle of cross-basin oscillation with east and west stops in JJA and DJF, respectively. 3) A well-defined prominent rainy zone is observed in the southeast China Seas around Taiwan Island, connecting with the Pacific rain pool in the south. 4) Between El Niño and La Niña years, there is a systematic sign reversal of the geographical distribution of precipitation anomaly, which exists globally rather than in the tropical oceans only. 5) On a global basis, interannual and annual precipitation variabilities are of the same magnitude, but the interannual (annual) component is more important for the Southern (Northern) Hemisphere. 6) For the tropical oceans, “season” defined by rainfall usually has a one-quarter delay with respect to the corresponding meteorological season. For the “marine deserts” in the subtropical oceans, however, the rain-based season is found to be anticorrelated with the meteorological season. In addition, the annual cycle of the Atlantic precipitation is nearly 180° out of phase with respect to that of the Pacific and Indian Ocean for the same hemisphere.

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Yundi Jiang
,
Wenjie Dong
,
Song Yang
, and
Jun Ma

Abstract

The authors quantitatively describe the changes in the characteristics of ice phenology including the flow rate and freeze/breakup dates of the Yellow River based on observations of the past 50 yr. In both the upper and lower reaches of the Yellow River, increasing temperature delays the freeze date and advances the breakup date, thus decreasing the number of freeze days and the expanse of river freeze. From 1968 to 2001, the freeze duration has shortened significantly by 38 days at Bayangaole and 25 days at Sanhuhe, respectively. From the early 1950s to the early 2000s, the changes in freeze and breakup dates have shortened the freeze duration in the lower reach of the Yellow River by 12 days. The flow rate has reduced from 500 to 260 m3 s−1, and the expanse of river freeze has also decreased significantly by about 310 km. In addition, in the lower reach of the river, the location of earliest ice breakup has shifted downstream significantly in the last 50 yr, although the location of earliest freeze exhibits little change.

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Sai Ma
,
Tianying Wang
,
Jun Yan
, and
Xuebin Zhang

Abstract

Climate change detection and attribution have played a central role in establishing the influence of human activities on climate. Optimal fingerprinting, a linear regression with errors in variables (EIVs), has been widely used in detection and attribution analyses of climate change. The method regresses observed climate variables on the expected climate responses to the external forcings, which are measured with EIVs. The reliability of the method depends critically on proper point and interval estimations of the regression coefficients. The confidence intervals constructed from the prevailing method, total least squares (TLS), have been reported to be too narrow to match their nominal confidence levels. We propose a novel framework to estimate the regression coefficients based on an efficient, bias-corrected estimating equations approach. The confidence intervals are constructed with a pseudo residual bootstrap variance estimator that takes advantage of the available control runs. Our regression coefficient estimator is unbiased, with a smaller variance than the TLS estimator. Our estimation of the sampling variability of the estimator has a low bias compared to that from TLS, which is substantially negatively biased. The resulting confidence intervals for the regression coefficients have coverage rates close to the nominal level, which ensures valid inferences in detection and attribution analyses. In applications to the annual mean near-surface air temperature at the global, continental, and subcontinental scales during 1951–2020, the proposed method led to shorter confidence intervals than those based on TLS in most of the analyses.

Significance Statement

Optimal fingerprinting is an important statistical tool for estimating human influences on the climate and for quantifying the associated uncertainty. Nonetheless, the estimators from the prevailing practice are not as optimal as believed, and their uncertainties are underestimated, both owing to the unreliable estimation of the optimal weight matrix that is critical to the method. Here we propose an estimation method based on the theory of estimating equations; to assess the uncertainty of the resulting estimator, we propose a pseudo bootstrap procedure. Through extensive numerical studies commonly used in statistical investigations, we demonstrate that the new estimator has a smaller mean-square error, and its uncertainty is estimated much closer to the true uncertainty than the prevailing total least squares method.

Open access
Kun Yang
,
Jun Qin
,
Xiaofeng Guo
,
Degang Zhou
, and
Yaoming Ma

Abstract

To clarify the thermal forcing of the Tibetan Plateau, long-term coarse-temporal-resolution data from the China Meteorological Administration have been widely used to estimate surface sensible heat flux by bulk methods in many previous studies; however, these estimates have seldom been evaluated against observations. This study at first evaluates three widely used bulk schemes against Tibet instrumental flux data. The evaluation shows that large uncertainties exist in the heat flux estimated by these schemes; in particular, upward heat fluxes in winter may be significantly underestimated, because diurnal variations of atmospheric stability were not taken into account. To improve the estimate, a new method is developed to disaggregate coarse-resolution meteorological data to hourly according to statistical relationships derived from high-resolution experimental data, and then sensible heat flux is estimated from the hourly data by a well-validated flux scheme. Evaluations against heat flux observations in summer and against net radiation observations in winter indicate that the new method performs much better than previous schemes, and therefore it provides a robust basis for quantifying the Tibetan surface energy budget.

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Stephen D. Eckermann
,
John Lindeman
,
Dave Broutman
,
Jun Ma
, and
Zafer Boybeyi

Abstract

Fully nonlinear mesoscale model simulations are used to investigate the momentum fluxes of gravity waves that emerge at a “far-field” height of 6 km from steady unsheared flow over both an axisymmetric and elliptical obstacle for nondimensional mountain heights ĥm = Fr−1 in the range 0.1–5, where Fr is the surface Froude number. Fourier- and Hilbert-transform diagnostics of model output yield local estimates of phase-averaged momentum flux, while area integrals of momentum flux quantify the amount of surface pressure drag that translates into far-field gravity waves, referred to here as the “wave drag” component. Estimates of surface and wave drag are compared to parameterization predictions and theory. Surface dynamics transition from linear to high-drag (wave breaking) states at critical inverse Froude numbers Fr c −1 predicted to within 10% by transform relations. Wave drag peaks at Fr c −1 < ĥm ≲ 2, where for the elliptical obstacle both surface and wave drag vacillate owing to cyclical buildup and breakdown of waves. For the axisymmetric obstacle, this occurs only at ĥm = 1.2. At ĥm ≳ 2–3 vacillation abates and normalized pressure drag assumes a common normalized form for both obstacles that varies approximately as ĥm −1.3. Wave drag in this range asymptotes to a constant absolute value that, despite its theoretical shortcomings, is predicted to within 10%–40% by an analytical relation based on linear clipped-obstacle drag for a Sheppard-based prediction of dividing streamline height. Constant wave drag at ĥm ∼ 2–5 arises despite large variations with ĥm in the three-dimensional morphology of the local wave momentum fluxes. Specific implications of these results for the parameterization of subgrid-scale orographic drag in global climate and weather models are discussed.

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Stephen D. Eckermann
,
Dave Broutman
,
Jun Ma
, and
John Lindeman

Abstract

A time-dependent generalization of a Fourier-ray method is presented and tested for fast numerical computation of high-resolution nonhydrostatic mountain-wave fields. The method is used to model mountain waves from Jan Mayen on 25 January 2000, a period when wavelike cloud banding was observed long distances downstream of the island by the Advanced Very High Resolution Radiometer Version 3 (AVHRR-3). Surface weather patterns show intensifying surface geostrophic winds over the island at 1200 UTC caused by rapid eastward passage of a compact low pressure system. The 1200 UTC wind profiles over the island increase with height to a jet maximum of ∼60–70 m s−1, yielding Scorer parameters that indicate vertical trapping of any short wavelength mountain waves. Separate Fourier-ray solutions were computed using high-resolution Jan Mayen orography and 1200 UTC vertical profiles of winds and temperatures over the island from a radiosonde sounding and an analysis system. The radiosonde-based simulations produce a purely diverging trapped wave solution that reproduces the salient features in the AVHRR-3 imagery. Differences in simulated wave patterns governed by the radiosonde and analysis profiles are explained in terms of resonant modes and are corroborated by spatial ray-group trajectories computed for wavenumbers along the resonant mode curves. Output from a nonlinear Lipps–Hemler orographic flow model also compares well with the Fourier-ray solution horizontally. Differences in vertical cross sections are ascribed to the Fourier-ray model’s current omission of tunneling of trapped wave energy through evanescent layers.

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Dave Broutman
,
Jun Ma
,
Stephen D. Eckermann
, and
John Lindeman

Abstract

The Fourier-ray method involves ray tracing in a Fourier-transform domain. The ray solutions are then Fourier synthesized to produce a spatial solution. Here previous steady-state developments of the Fourier-ray method are extended to include a transient source of mountain waves. The method is illustrated with an initial value problem in which the background flow is started abruptly from rest and then maintained at steady velocity. The resulting wave transience is modeled in a simple way. All rays that radiate from the mountain, including the initial rays, are assigned the full amplitude of the longtime steady-state solution. Time dependence comes in through the changing position of the initial rays. This is sufficient to account for wave transience in a test case, as demonstrated by comparison with simulations from a mesoscale numerical model.

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