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Stephen E. Lang
and
Wei-Kuo Tao

Abstract

The Goddard convective–stratiform heating (CSH) algorithm, used to estimate cloud heating in support of the Tropical Rainfall Measuring Mission (TRMM), is upgraded in support of the Global Precipitation Measurement (GPM) mission. The algorithm’s lookup tables (LUTs) are revised using new and additional cloud-resolving model (CRM) simulations from the Goddard Cumulus Ensemble (GCE) model, producing smoother heating patterns that span a wider range of intensities because of the increased sampling and finer GPM product grid. Low-level stratiform cooling rates are reduced in the land LUTs for a given rain intensity because of the rain evaporation correction in the new four-class ice (4ICE) scheme. Additional criteria, namely, echo-top heights and low-level reflectivity gradients, are tested for the selection of heating profiles. Those resulting LUTs show greater and more precise variation in their depth of heating as well as a tendency for stronger cooling and heating rates when low-level dBZ values decrease toward the surface. Comparisons versus TRMM for a 3-month period show much more low-level heating in the GPM retrievals because of increased detection of shallow convection, while upper-level heating patterns remain similar. The use of echo tops and low-level reflectivity gradients greatly reduces midlevel heating from ~2 to 5 km in the mean GPM heating profile, resulting in a more top-heavy profile like TRMM versus a more bottom-heavy profile with much more midlevel heating. Integrated latent heating rates are much better balanced versus surface rainfall for the GPM retrievals using the additional selection criteria with an overall bias of +4.3%.

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Stephen E. Lang
,
Wei-Kuo Tao
,
Xiping Zeng
, and
Yaping Li

Abstract

A well-known bias common to many bulk microphysics schemes currently being used in cloud-resolving models is the tendency to produce excessively large reflectivity values (e.g., 40 dBZ) in the middle and upper troposphere in simulated convective systems. The Rutledge and Hobbs–based bulk microphysics scheme in the Goddard Cumulus Ensemble model is modified to reduce this bias and improve realistic aspects. Modifications include lowering the efficiencies for snow/graupel riming and snow accreting cloud ice; converting less rimed snow to graupel; allowing snow/graupel sublimation; adding rime splintering, immersion freezing, and contact nucleation; replacing the Fletcher formulation for activated ice nuclei with that of Meyers et al.; allowing for ice supersaturation in the saturation adjustment; accounting for ambient RH in the growth of cloud ice to snow; and adding/accounting for cloud ice fall speeds. In addition, size-mapping schemes for snow/graupel were added as functions of temperature and mixing ratio, lowering particle sizes at colder temperatures but allowing larger particles near the melting level and at higher mixing ratios. The modifications were applied to a weakly organized continental case and an oceanic mesoscale convective system (MCS). Strong echoes in the middle and upper troposphere were reduced in both cases. Peak reflectivities agreed well with radar for the weaker land case but, despite improvement, remained too high for the MCS. Reflectivity distributions versus height were much improved versus radar for the less organized land case but not for the MCS despite fewer excessively strong echoes aloft due to a bias toward weaker echoes at storm top.

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Richard Ménard
,
Stephen E. Cohn
,
Lang-Ping Chang
, and
Peter M. Lyster

Abstract

The first part of this two-part article describes the formulation of a Kalman filter system for assimilating limb-sounding observations of stratospheric chemical constituents into a tracer transport model. The system is based on a two-dimensional isentropic approximation, permitting a full Kalman filter implementation and a thorough study of its behavior in a real-data environment. Datasets from two instruments on the Upper Atmosphere Research Satellite with very different viewing geometries are used in the assimilation experiments. A robust chi-squared diagnostic, which compares statistics of the observed-minus-forecast residuals with those calculated by the filter algorithm, is used to help formulate the statistical inputs to the filter, as well as to tune covariance parameters and to validate the assimilation results.

Two significant departures from the standard (discrete) Kalman filter formulation were found to be important in this study. First, it was discovered that the standard Kalman filter covariance propagation is highly inaccurate for this problem. Spurious and rapid loss of variance and increase of correlation length scales occur as a result of diffusion of the small-scale structures inherent in tracer error covariance fields. A new formulation based on well-understood properties of the continuum error covariance propagation was therefore introduced. Second, validation diagnostics suggested that the initial error, model error, and representativeness error are all more appropriately assumed to be relative than absolute in this problem. A filter formulation for relative errors was therefore devised. With these two modifications, this Kalman filter assimilation system has only three tunable variance parameters and one tunable correlation length-scale parameter.

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Steven E. Koch
,
F. Einaudi
,
Paul B. Dorian
,
Stephen Lang
, and
Gerald M. Heymsfield

Abstract

This paper summarizes the results of a detailed study from the Cooperative Convective Precipitation Experiment (CCOPE) of the vertical structure of mesoscale gravity waves that disturbed a sizable part of the troposphere and that played a significant role in the generation of a mesoscale convective complex. These bimodal waves displayed periods of 148 (50) min, wavelengths of 135 (60) km, and phase speeds of 15.2 (19.8) m s−1. A comparison is made between wave-induced pressure perturbation fields derived from triple-Doppler wind fields within regions of essentially nonconvective precipitation, pressure perturbation fields obtained by bandpass filtering of surface mesonetwork data, and the vertical structure of the pressure eigenfunctions as predicted from a linear stability analysis. It is believed that this represents the first such application of the Doppler radar pressure retrieval technique to the study of gravity waves. In addition, an analysis of the potential for shear instability was performed on all of the special CCOPE soundings taken on this day to determine the representativeness of the chosen soundings for the theoretical analysis and the likelihood that a wave maintenance mechanism endured throughout the 33-h wave event.

The analysis of the potential for shear instability and the eigenfunctions both indicate that the bimodal waves were able to efficiently extract energy from the mean flow near several closely spaced critical levels in the 4.0– 6.5-km layer to maintain their coherence for many wave cycles. This result serves as the explanation for the observed ability of the waves to organize precipitation into long convective bands whose axes were along and just ahead of the wave crests. The eigenvalue analysis predicts unstable modes that are hydrostatic, nondispersive, ducted gravity waves characterized by half of a vertical wavelength contained between the ground and the lowest critical level (at z = 4 km). Eigenfunctions of pressure and other variables all display negligible tilt below 2.3–3.3 km, above which a sudden reversal in phase occurs.

The vertical structure of the Doppler-derived fields associated with one of these gravity waves agrees in terms of the following respects with the eigenfunction predictions and/or the surface mesoanalyses: (a) the vertical wavelength, horizontal structure, and amplitude of the perturbation horizontal wind and pressure fields, and (b) the in-phase covariance between the pressure and horizontal wind fields at levels below 2.5 km. On the other hand, the theory predicted a much more abrupt vertical transition in phase in the pressure fields and weaker amplitudes aloft than were evident in the Doppler analyses. In addition, the size of the multiple-Doppler analysis domain was too small to capture an entire horizontal wavelength of the 135-km-scale gravity wave, which made direct comparisons difficult. Furthermore, the linear theory predicts much smaller amplitudes and somewhat longer horizontal wavelengths for the vertical motions characterizing both wave modes than those seen in the Doppler winds, which likely also contain nonwave effects. These discrepancies are largely due to the combined effects of weak convection, turbulence, and data sampling problems. Despite these drawbacks, the findings from this and other recent studies using Doppler radars and ground-based radiometers suggest that remote sensing of mesoscale gravity waves that occupy a significant fraction of the troposphere should be exploited further.

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Stephen E. Lang
,
Wei-Kuo Tao
,
Jiun-Dar Chern
,
Di Wu
, and
Xiaowen Li

Abstract

Current cloud microphysical schemes used in cloud and mesoscale models range from simple one-moment to multimoment, multiclass to explicit bin schemes. This study details the benefits of adding a fourth ice class (frozen drops/hail) to an already improved single-moment three-class ice (cloud ice, snow, graupel) bulk microphysics scheme developed for the Goddard Cumulus Ensemble model. Besides the addition and modification of several hail processes from a bulk three-class hail scheme, further modifications were made to the three-ice processes, including allowing greater ice supersaturation and mitigating spurious evaporation/sublimation in the saturation adjustment scheme, allowing graupel/hail to transition to snow via vapor growth and hail to transition to graupel via riming, wet graupel to become hail, and the inclusion of a rain evaporation correction and vapor diffusivity factor. The improved three-ice snow/graupel size-mapping schemes were adjusted to be more stable at higher mixing ratios and to increase the aggregation effect for snow. A snow density mapping was also added.

The new scheme was applied to an intense continental squall line and a moderate, loosely organized continental case using three different hail intercepts. Peak simulated reflectivities agree well with radar for both the intense and moderate cases and were superior to earlier three-ice versions when using a moderate and large intercept for hail, respectively. Simulated reflectivity distributions versus height were also improved versus radar in both cases compared to earlier three-ice versions. The bin-based rain evaporation correction affected the squall line more but overall the agreement among the reflectivity distributions was unchanged. The new scheme also improved the simulated surface rain-rate histograms.

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Angela K. Rowe
,
Steven A. Rutledge
,
Timothy J. Lang
,
Paul E. Ciesielski
, and
Stephen M. Saleeby

Abstract

Radar data from the 2004 North American Monsoon Experiment (NAME) enhanced observing period were used to investigate diurnal trends and vertical structure of precipitating features relative to local terrain. Two-dimensional composites of reflectivity and rain rate, created from the two Servicio Meteorológico Nacional (SMN; Mexican Weather Service) C-band Doppler radars and NCAR’s S-band polarimetric Doppler radar (S-Pol), were divided into four elevation groups: over water, 0–1000 m (MSL), 1000–2000 m, and greater than 2000 m. Analysis of precipitation frequency and average rainfall intensity using these composites reveals a strong diurnal trend in precipitation similar to that observed by the NAME Event Rain Gauge Network. Precipitation occurs most frequently during the afternoon over the Sierra Madre Occidental (SMO), with the peak frequency moving over the lower elevations by evening. Also, the precipitation events over the lower elevations are less frequent but of greater intensity (rain rate) than those over the SMO. Precipitation echoes were partitioned into convective and stratiform components to allow for examination of vertical characteristics of convection using data from S-Pol. Analyses of reflectivity profiles and echo-top heights confirm that convection over the lower terrain is more intense and vertically developed than convection over the SMO. Warm-cloud depths, estimated from the Colorado State University–NAME upper-air and surface gridded analyses are, on average, 2 times as deep over the lower terrain as compared with over the SMO. Using a simplified stochastic model for drop growth, it is shown that these differences in warm-cloud depths could possibly explain the observed elevation-dependent trends in precipitation intensity.

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Timothy J. Lang
,
David A. Ahijevych
,
Stephen W. Nesbitt
,
Richard E. Carbone
,
Steven A. Rutledge
, and
Robert Cifelli

Abstract

A multiradar network, operated in the southern Gulf of California (GoC) region during the 2004 North American Monsoon Experiment, is used to analyze the spatial and temporal variabilities of local precipitation. Based on the initial findings of this analysis, it is found that terrain played a key role in this variability, as the diurnal cycle was dominated by convective triggering during the afternoon over the peaks and foothills of the Sierra Madre Occidental (SMO). Precipitating systems grew upscale and moved WNW toward the gulf. Distinct precipitation regimes within the monsoon are identified. The first, regime A, corresponded to enhanced precipitation over the southern portions of the coast and GoC, typically during the overnight and early morning hours. This was due to precipitating systems surviving the westward trip (∼7 m s−1; 3–4 m s−1 in excess of steering winds) from the SMO after sunset, likely because of enhanced environmental wind shear as diagnosed from local soundings. The second, regime B, corresponded to the significant northward/along-coast movement of systems (∼10 m s−1; 4–5 m s−1 in excess of steering winds) and often overlapped with regime A. The weak propagation is explainable by shallow–weak cold pools. Reanalysis data suggest that tropical easterly waves were associated with the occurrence of disturbed regimes. Gulf surges occurred during a small subset of these regimes, so they played a minor role during 2004. Mesoscale convective systems and other organized systems were responsible for most of the rainfall in this region, particularly during the disturbed regimes.

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William S. Olson
,
Christian D. Kummerow
,
Song Yang
,
Grant W. Petty
,
Wei-Kuo Tao
,
Thomas L. Bell
,
Scott A. Braun
,
Yansen Wang
,
Stephen E. Lang
,
Daniel E. Johnson
, and
Christine Chiu

Abstract

A revised Bayesian algorithm for estimating surface rain rate, convective rain proportion, and latent heating profiles from satellite-borne passive microwave radiometer observations over ocean backgrounds is described. The algorithm searches a large database of cloud-radiative model simulations to find cloud profiles that are radiatively consistent with a given set of microwave radiance measurements. The properties of these radiatively consistent profiles are then composited to obtain best estimates of the observed properties. The revised algorithm is supported by an expanded and more physically consistent database of cloud-radiative model simulations. The algorithm also features a better quantification of the convective and nonconvective contributions to total rainfall, a new geographic database, and an improved representation of background radiances in rain-free regions. Bias and random error estimates are derived from applications of the algorithm to synthetic radiance data, based upon a subset of cloud-resolving model simulations, and from the Bayesian formulation itself. Synthetic rain-rate and latent heating estimates exhibit a trend of high (low) bias for low (high) retrieved values. The Bayesian estimates of random error are propagated to represent errors at coarser time and space resolutions, based upon applications of the algorithm to TRMM Microwave Imager (TMI) data. Errors in TMI instantaneous rain-rate estimates at 0.5°-resolution range from approximately 50% at 1 mm h−1 to 20% at 14 mm h−1. Errors in collocated spaceborne radar rain-rate estimates are roughly 50%–80% of the TMI errors at this resolution. The estimated algorithm random error in TMI rain rates at monthly, 2.5° resolution is relatively small (less than 6% at 5 mm day−1) in comparison with the random error resulting from infrequent satellite temporal sampling (8%–35% at the same rain rate). Percentage errors resulting from sampling decrease with increasing rain rate, and sampling errors in latent heating rates follow the same trend. Averaging over 3 months reduces sampling errors in rain rates to 6%–15% at 5 mm day−1, with proportionate reductions in latent heating sampling errors.

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Xianan Jiang
,
Duane E. Waliser
,
William S. Olson
,
Wei-Kuo Tao
,
Tristan S. L’Ecuyer
,
Jui-Lin Li
,
Baijun Tian
,
Yuk L. Yung
,
Adrian M. Tompkins
,
Stephen E. Lang
, and
Mircea Grecu

Abstract

The Madden–Julian oscillation (MJO) is a fundamental mode of the tropical atmosphere variability that exerts significant influence on global climate and weather systems. Current global circulation models, unfortunately, are incapable of robustly representing this form of variability. Meanwhile, a well-accepted and comprehensive theory for the MJO is still elusive. To help address this challenge, recent emphasis has been placed on characterizing the vertical structures of the MJO. In this study, the authors analyze vertical heating structures by utilizing recently updated heating estimates based on the Tropical Rainfall Measuring Mission (TRMM) from two different latent heating estimates and one radiative heating estimate. Heating structures from two different versions of the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalyses/forecasts are also examined. Because of the limited period of available datasets at the time of this study, the authors focus on the winter season from October 1998 to March 1999.

The results suggest that diabatic heating associated with the MJO convection in the ECMWF outputs exhibits much stronger amplitude and deeper structures than that in the TRMM estimates over the equatorial eastern Indian Ocean and western Pacific. Further analysis illustrates that this difference might be due to stronger convective and weaker stratiform components in the ECMWF estimates relative to the TRMM estimates, with the latter suggesting a comparable contribution by the stratiform and convective counterparts in contributing to the total rain rate. Based on the TRMM estimates, it is also illustrated that the stratiform fraction of total rain rate varies with the evolution of the MJO. Stratiform rain ratio over the Indian Ocean is found to be 5% above (below) average for the disturbed (suppressed) phase of the MJO. The results are discussed with respect to whether these heating estimates provide enough convergent information to have implications on theories of the MJO and whether they can help validate global weather and climate models.

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Xianan Jiang
,
Duane E. Waliser
,
William S. Olson
,
Wei-Kuo Tao
,
Tristan S. L’Ecuyer
,
King-Fai Li
,
Yuk L. Yung
,
Shoichi Shige
,
Stephen Lang
, and
Yukari N. Takayabu

Abstract

Capitalizing on recently released reanalysis datasets and diabatic heating estimates based on Tropical Rainfall Measuring Mission (TRMM), the authors have conducted a composite analysis of vertical anomalous heating structures associated with the Madden–Julian oscillation (MJO). Because diabatic heating lies at the heart of prevailing MJO theories, the intention of this effort is to provide new insights into the fundamental physics of the MJO. However, some discrepancies in the composite vertical MJO heating profiles are noted among the datasets, particularly between three reanalyses and three TRMM estimates. A westward tilting with altitude in the vertical heating structure of the MJO is clearly evident during its eastward propagation based on three reanalysis datasets, which is particularly pronounced when the MJO migrates from the equatorial eastern Indian Ocean (EEIO) to the western Pacific (WP). In contrast, this vertical tilt in heating structure is not readily seen in the three TRMM products. Moreover, a transition from a shallow to deep heating structure associated with the MJO is clearly evident in a pressure–time plot over both the EEIO and WP in three reanalysis datasets. Although this vertical heating structure transition is detectable over the WP in two TRMM products, it is weakly defined in another dataset over the WP and in all three TRMM datasets over the EEIO.

The vertical structures of radiative heating QR associated with the MJO are also analyzed based on TRMM and two reanalysis datasets. A westward vertical tilt in QR is apparent in all these datasets: that is, the low-level QR is largely in phase of convection, whereas QR in the upper troposphere lags the maximum convection. The results also suggest a potentially important role of radiative heating for the MJO, particularly over the Indian Ocean. Caveats in heating estimates based on both the reanalysis datasets and TRMM are briefly discussed.

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