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Fiaz Ahmed

Abstract

Linearized wave solutions on the equatorial beta plane are examined in the presence of a background meridional moisture gradient. Of interest is a slow, eastward-propagating n = 1 mode that is unstable at planetary scales and only exists for a small range of zonal wavenumbers (6). The mode dispersion curve appears as an eastward extension of the westward-propagating equatorial Rossby wave solution. This mode is therefore termed the eastward-propagating equatorial Rossby wave (ERW). The zonal wavenumber-2 ERW horizontal structure consists of a low-level equatorial convergence center flanked by quadrupole off-equatorial gyres, and resembles the horizontal structure of the observed MJO. An analytic, leading-order dispersion relationship for the ERW shows that meridional moisture advection imparts eastward propagation, and that the smallness of a gross moist stability–like parameter contributes to the slow phase speed. The ERW is unstable near planetary scales when low-level easterlies moisten the column. This moistening could come from either zonal moisture advection or surface fluxes or a combination thereof. When westerlies instead moisten the column, the ERW is damped and the westward-propagating long Rossby wave is unstable. The ERW does not exist when the meridional moisture gradient is too weak. A moist static energy budget analysis shows that the ERW scale selection is partly due to finite-time-scale convective adjustment and less effective zonal wind–induced moistening at smaller scales. Similarities in the phase speed, preferred scale, and horizontal structure suggest that the ERW is a beta-plane analog of the MJO.

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Fiaz Ahmed and Courtney Schumacher

Abstract

Positive feedbacks between the cloud population and the environmental moisture field are central to theoretical expositions on the Madden–Julian oscillation (MJO). This study investigates the statistical incidence of positive moisture–convection feedbacks across multiple space and time scales over the tropical Indian Ocean. This work uses vertically integrated moisture budget terms from the ECMWF interim reanalysis [ERA-Interim (ERA-I)] in a framework proposed by Hannah et al. Positive moisture–convection feedbacks are primarily a low-frequency, low-wavenumber phenomenon with significant spectral signatures in the 32–48-day time scale. The efficacy of these feedbacks, however, is subject to horizontal moisture advection variations, whose relative importance varies with scale. Wave-filtered Tropical Rainfall Measuring Mission (TRMM) satellite precipitation is used to show that these moisture–convection feedbacks contribute more to moisture increases in the MJO than in other equatorial waves. A moving-window correlation analysis suggests that instances of moisture–convection feedbacks are more frequent in drier conditions, when column water vapor (CWV) is below its climatological mean value, with the implication that positive moisture–convection feedbacks shape the mean CWV field by moistening drier air columns, but that they are less effective in moistening already moist environments. Ground radar observations show that stratiform rain damps local CWV increases on short time scales (<2 days) and therefore precludes positive moisture–convection feedbacks in high-CWV environments. Vertical coherence structures from ERA-I confirm that relatively bottom-heavy cloud ensembles (i.e., peaks between 700 and 850 hPa) are more effective in inducing low-frequency positive moisture–convection feedbacks than ensembles with other vertical structures. Low-frequency horizontal advective drying damps moisture increases and is strongly coherent with upper-level rising motion.

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Fiaz Ahmed and J. David Neelin

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Precipitation clusters are contiguous raining regions characterized by a precipitation threshold, size, and the total rainfall contained within—termed the cluster power. Tropical observations suggest that the probability distributions of both cluster size and power contain a power-law range (with slope ~ −1.5) bounded by a large-event “cutoff.” Events with values beyond the cutoff signify large, powerful clusters and represent extreme events. A two-dimensional stochastic model is introduced to reproduce the observed cluster distributions, including the slope and the cutoff. The model is equipped with coupled moisture and weak temperature gradient (WTG) energy equations, empirically motivated precipitation parameterization, temporally persistent noise, and lateral mixing processes, all of which collectively shape the model cluster distributions. Moisture–radiative feedbacks aid clustering, but excessively strong feedbacks push the model into a self-aggregating regime. The power-law slope is stable in a realistic parameter range. The cutoff is sensitive to multiple model parameters including the stochastic forcing amplitude, the threshold moisture value that triggers precipitation, and the lateral mixing efficiency. Among the candidates for simple analogs of precipitation clustering, percolation models are ruled out as unsatisfactory, but the stochastic branching process proves useful in formulating a neighbor probability metric. This metric measures the average number of nearest neighbors that a precipitating entity can spawn per time interval and captures the cutoff parameter sensitivity for both cluster size and power. The results here suggest that the clustering tendency and the horizontal scale limiting large tropical precipitating systems arise from aggregate effects of multiple moist processes, which are encapsulated in the neighbor probability metric.

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Fiaz Ahmed and J. David Neelin

Abstract

The tropical precipitation–moisture relationship, characterized by rapid increases in precipitation for modest increases in moisture, is conceptually recast in a framework relevant to plume buoyancy and conditional instability in the tropics. The working hypothesis in this framework links the rapid onset of precipitation to integrated buoyancy in the lower troposphere. An analytical expression that relates the buoyancy of an entraining plume to the vertical thermodynamic structure is derived. The natural variables in this framework are saturation and subsaturation equivalent potential temperatures, which capture the leading-order temperature and moisture variations, respectively. The use of layer averages simplifies the analytical and subsequent numerical treatment. Three distinct layers, the boundary layer, the lower free troposphere, and the midtroposphere, adequately capture the vertical variations in the thermodynamic structure. The influence of each environmental layer on the plume is assumed to occur via lateral entrainment, corresponding to an assumed mass-flux profile. The fractional contribution of each layer to the midlevel plume buoyancy (i.e., the layer weight) is estimated from TRMM 3B42 precipitation and ERA-Interim thermodynamic profiles. The layer weights are used to “reverse engineer” a deep-inflow mass-flux profile that is nominally descriptive of the tropical atmosphere through the onset of deep convection. The layer weights—which are nearly the same for each of the layers—constitute an environmental influence function and are also used to compute a free-tropospheric integrated buoyancy measure. This measure is shown to be an effective predictor of onset in conditionally averaged precipitation across the global tropics—over both land and ocean.

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Fiaz Ahmed and J. David Neelin

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Entrainment of dry tropospheric air can dilute cloud buoyancies and strongly affect the occurrence and intensity of convection. To measure this dry air influence on tropical precipitation, rainfall values that would occur when convection is ‘protected’ from dry air dilution are estimated. An empirical relationship between tropical oceanic precipitation and entraining buoyancy in the lower troposphere (surface-600 hPa) is leveraged. Protected buoyancies are computed by allowing a plume model to entrain saturated air at environmental temperature. These buoyancies are then used to estimate precipitation from protected convection. In most regions, the protected precipitation greatly exceeds the observed precipitation. Warm waters adjoining continents display striking disparities between observed and protected rainfall pointing to rainfall climatologies severely limited by dry air. The most prominent of these regions include the Red Sea and the Persian Gulf, followed by the Caribbean Sea, the Gulf of Mexico, and the seas surrounding the Maritime Continent. We test if similar large precipitation values are realizable in the Community Atmospheric Model (CAM5), wherein the parameterized convection in small (∼ 2°×2°) pockets is allowed to only entrain saturated air. The precipitation within these pockets shows strong enhancement that is maintained over time, and is compensated by slight reductions in neighboring regions. In the model, protecting convection yields larger precipitation values over ocean than over land; protected precipitation also intensifies in a uniform SST warming experiment. The model experiments suggest that protected pockets in numerical simulations could be used to mimic the consequences of meteorological protection—from closed circulation or moisture shielding effects—that generate extreme precipitation.

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Fiaz Ahmed and J. David Neelin

Abstract

Entrainment of dry tropospheric air can dilute cloud buoyancies and strongly affect the occurrence and intensity of convection. To measure this dry air influence on tropical precipitation, rainfall values that would occur when convection is “protected” from dry air dilution are estimated. An empirical relationship between tropical oceanic precipitation and entraining buoyancy in the lower troposphere (from the surface to 600 hPa) is leveraged. Protected buoyancies are computed by allowing a plume model to entrain saturated air at environmental temperature. These buoyancies are then used to estimate precipitation from protected convection. In most regions, the protected precipitation greatly exceeds the observed precipitation. Warm waters adjoining continents display striking disparities between observed and protected rainfall pointing to rainfall climatologies severely limited by dry air. The most prominent of these regions include the Red Sea and the Persian Gulf, followed by the Caribbean Sea, the Gulf of Mexico, and the seas surrounding the Maritime Continent. We test if similar large precipitation values are realizable in the Community Atmospheric Model (CAM5), wherein the parameterized convection in small (~2° × 2°) pockets is allowed to only entrain saturated air. The precipitation within these pockets shows strong enhancement that is maintained over time, and is compensated by slight reductions in neighboring regions. In the model, protecting convection yields larger precipitation values over ocean than over land; protected precipitation also intensifies in a uniform SST warming experiment. The model experiments suggest that protected pockets in numerical simulations could be used to mimic the consequences of meteorological protection—from closed circulation or moisture shielding effects—that generate extreme precipitation.

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Fiaz Ahmed, Courtney Schumacher, Zhe Feng, and Samson Hagos

Abstract

Radar-based latent heating retrievals typically apply a lookup table (LUT) derived from model output to surface rain amounts and rain type to determine the vertical structure of heating. In this study, a method has been developed that uses the size characteristics of precipitating systems (i.e., area and mean echo-top height) instead of rain amount to estimate latent heating profiles from radar observations. This technique [named the convective–stratiform area (CSA) algorithm] leverages the relationship between the organization of convective systems and the structure of latent heating profiles and avoids pitfalls associated with retrieving accurate rainfall information from radars and models. The CSA LUTs are based on a high-resolution regional model simulation over the equatorial Indian Ocean. The CSA LUTs show that convective latent heating increases in magnitude and height as area and echo-top heights grow, with a congestus signature of midlevel cooling for less vertically extensive convective systems. Stratiform latent heating varies weakly in vertical structure, but its magnitude is strongly linked to area and mean echo-top heights. The CSA LUT was applied to radar observations collected during the DYNAMO/Cooperative Indian Ocean Experiment on Intraseasonal Variability in the Year 2011 (CINDY2011)/ARM MJO Investigation Experiment (AMIE) field campaign, and the CSA heating retrieval was generally consistent with other measures of heating profiles. The impact of resolution and spatial mismatch between the model and radar grids is addressed, and unrealistic latent heating profiles in the stratiform LUT, namely, a low-level heating peak, an elevated melting layer, and net column cooling, were identified. These issues highlight the need for accurate convective–stratiform separations and improvement in PBL and microphysical parameterizations.

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Fiaz Ahmed, J. David Neelin, and Ángel F. Adames

Abstract

Convective quasi-equilibrium (QE) and weak temperature gradient (WTG) balances are frequently employed to study the tropical atmosphere. This study uses linearized equatorial beta-plane solutions to examine the relevant regimes for these balances. Wave solutions are characterized by moisture–temperature ratio (qT ratio) and dominant thermodynamic balances. An empirically constrained precipitation closure assigns different sensitivities of convection to temperature (ε t) and moisture (ε q). Longwave equatorial Kelvin and Rossby waves tend toward the QE balance with qT ratios of ε t:ε q that can be ~1–3. Departures from strict QE, essential to both precipitation and wave dynamics, grow with wavenumber. The propagating QE modes have reduced phase speeds because of the effective gross moist stability m eff, with a further reduction when ε t > 0. Moisture modes obeying the WTG balance and with large qT ratios (>10) emerge in the shortwave regime; these modes exist with both Kelvin and Rossby wave meridional structures. In the υ = 0 case, long propagating gravity waves are absent and only emerge beyond a cutoff wavenumber. Two bifurcations in the wave solutions are identified and used to locate the spatial scales for QE–WTG transition and gravity wave emergence. These scales are governed by the competition between the convection and gravity wave adjustment times and are modulated by m eff. Near-zero values of m eff shift the QE–WTG transition wavenumber toward zero. Continuous transitions replace the bifurcations when m eff < 0 or moisture advection/WISHE mechanisms are included, but the wavenumber-dependent QE and WTG balances remain qualitatively unaltered. Rapidly decaying convective/gravity wave modes adjust to the slowly evolving QE/WTG state in the longwave/shortwave regimes, respectively.

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Fiaz Ahmed, Ángel F. Adames, and J. David Neelin

Abstract

Simple process models and complex climate models are remarkably sensitive to the time scale of convective adjustment τ, but this parameter remains poorly constrained and understood. This study uses the linear-range slope of a semiempirical relationship between precipitation and a lower-free-tropospheric buoyancy measure B L. The B L measure is a function of layer-averaged moist enthalpy in the boundary layer (150-hPa-thick layer above surface), and temperature and moisture in the lower free troposphere (boundary layer top to 500 hPa). Sensitivity parameters with units of time quantify the B L response to its component perturbations. In moist enthalpy units, B L is more sensitive to temperature than equivalent moisture perturbations. However, column-integrated moist static energy conservation ensures that temperature and moisture are equally altered during the adjustment process. Multiple adjusted states with different temperature–moisture combinations exist; the B L sensitivity parameters govern the relationship between adjusted states, and also combine to yield a time scale of convective adjustment ~2 h. This value is comparable to τ values used in cumulus parameterization closures. Disparities in previously reported values of τ are attributed to the neglect of the temperature contribution to precipitation, and to averaging operations that include data from both precipitating and nonprecipitating regimes. A stochastic model of tropical convection demonstrates how either averaging operations or neglected environmental influences on precipitation can yield τ estimates longer than the true τ value built into the model. The analysis here culminates in construction of a precipitation closure with both moisture and temperature adjustment (qT closure), suitable for use in both linearized and nonlinear, intermediate-complexity models.

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Brandon Wolding, Scott W. Powell, Fiaz Ahmed, Juliana Dias, Maria Gehne, George Kiladis, and J. David Neelin

Abstract

This study examines thermodynamic-convection coupling in observations and re-analyses, and attempts to establish process level benchmarks needed to guide model development. Thermodynamic profiles obtained from the NOAA Integrated Global Radiosonde Archive, COSMIC-1 GPS radio occultations, and several reanalyses are examined alongside Tropical Rain-fall Measuring Mission precipitation estimates. Cyclical increases and decreases in a bulk measure of lower tropospheric convective instability are shown to be coupled to the cyclical amplification and decay of convection. This cyclical flow emerges from conditional-mean analysis in a thermodynamic space comprised of two components: a measure of “undiluted” instability which neglects lower free tropospheric (LFT) entrainment, and a measure of the reduction of instability by LFT entrainment. The observational and reanalysis products examined share the following qualitatively robust characterization of these convective cycles: increases in undiluted instability tend to occur when the LFT is less saturated, are followed by increases in LFT saturation and precipitation rate, which are then followed by decreases in undiluted instability. Shallow, convective and stratiform precipitation are coupled to these cycles in a manner consistent with meteorological expectations. In situ and satellite observations differ systematically from reanalyses in their depictions of lower tropospheric temperature and moisture variations throughout these convective cycles. When using reanalysis thermodynamic fields, these systematic differences cause variations in lower free tropospheric saturation deficit to appear less influential in determining the strength of convection than is suggested by observations. Disagreements amongst reanalyses, as well as between reanalyses and observations, pose significant challenges to process level assessments of thermodynamic-convection coupling.

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