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John Lewis
and
S. Lakshmivarahan

Abstract

Yoshikazu Sasaki developed a variational method of data assimilation, a cornerstone of modern-day analysis and prediction in meteorology. Fundamentally, he formulated data assimilation as a constrained minimization problem with equality constraints. The generation of this idea is tracked by analyzing his education and research at the University of Tokyo in the immediate post–World War II (WWII) period. Despite austere circumstances—including limited financial support for education, poor living conditions, and a lack of educational resources—Sasaki was highly motivated and overcame these obstacles on his path to developing this innovative method of weather map analysis. The stages of his intellectual development are followed where information comes from access to his early publications, oral histories, and letters of reminiscence.

It has been argued that Sasaki’s unique contribution to meteorological data assimilation stems from his deterministic view of the problem—a view founded on the principles of variational mechanics. Sasaki’s approach to the problem is compared and contrasted with the stochastic view that was pioneered by Arnt Eliassen. Both of these optimal approaches are viewed in the context of the pragmatic–operational objective analysis schemes that were developed in the 1950s–1960s. Finally, current-day methods [e.g., three- and four-dimensional variational data assimilation (3DVAR and 4DVAR)] are linked to the optimal methods of Eliassen and Sasaki.

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John S. Lewis

Abstract

No abstract available.

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John S. Lewis

Abstract

The enthalpy change in chemical reactions between atmospheric CO2 and Venus surface rocks is shown to provide an extremely effective mechanism for damping short-term temperature excursions in the lower atmosphere. It is shown that the diurnal temperature variation near the Venus equator is probably less than 0.05K

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Kenneth A. Goettel
and
John S. Lewis

Abstract

Several aspects of the chemistry of NH3 in the Venus atmosphere are examined. Production of NH3 and precipitation of NH3 compounds are considered quantitatively. It is concluded that the high NH3 mixing ratios reported by the Soviet Venera 8 landing probe appear to be inconsistent with the observed abundances of other gases in the Venus atmosphere.

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John M. Lewis
and
S. Lakshmivarahan

Abstract

A single-day meeting between two theoretical meteorologists took place in 1961 at the Travelers Research Center (TRC) in Hartford, Connecticut. The two scientists were Barry Saltzman and Edward Lorenz, former proteges of V. P. Starr at MIT. Several years before this meeting, Lorenz discovered the following profound result: extended-range weather forecasting was not feasible in the presence of slight errors in initial conditions. The model used was the geostrophic form of a two-level baroclinic model with twelve spectral variables. These results were presented a year earlier at the First Symposium on Numerical Weather Prediction (NWP) in Tokyo, Japan, and met with some skepticism from the NWP elite, dynamical meteorologists, and pioneers in operational NWP. Lorenz held faint hope that Saltzman’s recently developed model of Rayleigh- Bénard convection would produce the profound result found earlier. One of the numerical experiments executed that eventful day with Saltzman’s 7-mode truncated spectral model produced an unexpected result: inability of the model’s 7 variables to settle down and approach a steady state. This occurred when the key parameter, the Rayleigh number, assumed an especially large value, one associated with turbulent convection. And further experimentation with the case delivered the sought-after result that Lorenz had found earlier, and now convincingly found with a simpler model. It built the bridge to chaos theory. The pathway to this exceptional result is explored by revisiting Saltzman’s and Lorenz’s mentorship under V. P. Starr, the authors’ interview with Lorenz in 2002 that complements information in Lorenz’s scientific autobiography, and the authors’ published perspective on Salzman’s 7-mode model.

Open access
S. Lakshmivarahan
,
John M. Lewis
, and
Junjun Hu

Abstract

In Saltzman’s seminal paper from 1962, the author developed a framework based on the spectral method for the analysis of the solution to the classical Rayleigh–Bénard convection problem using low-order models (LOMs), LOM (n) with n ≤ 52. By way of illustrating the power of these models, he singled out an LOM (7) and presented a very preliminary account of its numerical solution starting from one initial condition and for two values of the Rayleigh number, λ = 2 and 5. This paper provides a complete mathematical characterization of the solution of this LOM (7), herein called the Saltzman LOM (7) [S-LOM (7)]. Historically, Saltzman’s examination of the numerical solution of this low-order model contained two salient characteristics: 1) the periodic solution (in the physical 3D space and time) that expand on Rayleigh’s classical study and 2) a nonperiodic solution (in the temporal space dealing with the evolution of Fourier amplitude) that served Lorenz in his fundamental study of chaos in the early 1960s. Interestingly, the presence of this nonperiodic solution was left unmentioned in Saltzman’s study in 1962 but explained in detail in Lorenz’s scientific biography in 1993. Both of these fundamental aspects of Saltzman’s study are fully explored in this paper and bring a sense of completeness to the work.

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S. Lakshmivarahan
,
John M. Lewis
, and
Junjun Hu

Abstract

Over the decades the role of observations in building and/or improving the fidelity of a model to a phenomenon is well documented in the meteorological literature. More recently adaptive/targeted observations have been routinely used to improve the quality of the analysis resulting from the fusion of data with models in a data assimilation scheme and the subsequent forecast. In this paper our goal is to develop an offline (preprocessing) diagnostic strategy for placing observations with a singular view to reduce the forecast error/innovation in the context of the classical 4D-Var. It is well known that the shape of the cost functional as measured by its gradient (also called adjoint gradient or sensitivity) in the control (initial condition and model parameters) space determines the marching of the control iterates toward a local minimum. These iterates can become marooned in regions of control space where the gradient is small. An open question is how to avoid these “flat” regions by bounding the norm of the gradient away from zero. We answer this question in two steps. We, for the first time, derive a linear transformation defined by a symmetric positive semidefinite (SPSD) Gramian G = F ¯ T F ¯ that directly relates the control error to the adjoint gradient. It is then shown that by placing observations where the square of the Frobenius norm of F ¯ (which is also the sum of the eigenvalues of G ) is a maximum, we can indeed bound the norm of the adjoint gradient away from zero.

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Pedro N. DiNezio
,
Lewis J. Gramer
,
William E. Johns
,
Christopher S. Meinen
, and
Molly O. Baringer

Abstract

The role of wind stress curl (WSC) forcing in the observed interannual variability of the Florida Current (FC) transport is investigated. Evidence is provided for baroclinic adjustment as a physical mechanism linking interannual changes in WSC forcing and changes in the circulation of the North Atlantic subtropical gyre. A continuous monthly time series of FC transport is constructed using daily transports estimated from undersea telephone cables near 27°N in the Straits of Florida. This 25-yr-long time series is linearly regressed against interannual WSC variability derived from the NCEP–NCAR reanalysis. The results indicate that a substantial fraction of the FC transport variability at 3–12-yr periods is explained by low-frequency WSC variations. A lagged regression analysis is performed to explore hypothetical adjustment times of the wind-driven circulation. The estimated lag times are at least 2 times faster than those predicted by linear beta-plane planetary wave theory. Possible reasons for this discrepancy are discussed within the context of recent observational and theoretical developments. The results are then linked with earlier findings of a low-frequency anticorrelation between FC transport and the North Atlantic Oscillation (NAO) index, showing that this relationship could result from the positive (negative) WSC anomalies that develop between 20° and 30°N in the western North Atlantic during high (low) NAO phases. Ultimately, the observed role of wind forcing on the interannual variability of the FC could represent a benchmark for current efforts to monitor and predict the North Atlantic circulation.

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John T. Van Stan II
,
Ethan D. Gutmann
,
Elliott S. Lewis
, and
Trent E. Gay

Abstract

Barrier island forests are sensitive to changing precipitation characteristics as they typically rely on a precipitation-fed freshwater lens. Understanding and predicting significant rainfall losses is, therefore, critical to the prediction and management of hydrometeorological processes in the barrier island forest ecosystem. This study measures and models one such loss, canopy rainfall interception, for a barrier island forest common across subtropical and tropical coastlines: epiphyte-laden Quercus virginiana on St. Catherine’s Island (Georgia, United States). Reformulated Gash analytical models (RGAMs) relying on static- and variable-canopy-storage formulations were parameterized using common maximum water storage (minimum, mean, maximum, and laboratory submersion) and evaporation (Penman–Monteith, saturated rain–throughfall regression, and rain–interception regression) estimation methods. Cumulative interception loss was 37% of rainfall, and the epiphyte community contribution to interception loss was 11%. Variable-storage RGAMs using inferred evaporation and maximum water storage estimates performed best: mean absolute error of 1–2 mm, normalized mean percent error of 15%–25%, and model efficiency of 0.88–0.97, resulting in a 2%–5% overestimate of cumulative interception. Static- and variable-storage RGAMs using physically derived evaporation (Penman–Monteith) underestimated observed interception loss (40%–60%), yet the error was significantly lowered for submersion estimates of maximum water storage. Greater apparent error when using Penman–Monteith rates may result from unknown drying times, evaporation sources, and/or in situ epiphyte storage dynamics. As such, it is suggested that future research apply existing technologies to quantify evaporative processes during rainfall (e.g., eddy covariance) and to develop new methods to directly monitor in situ epiphyte water storage.

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Michael L. Kaplan
,
Christopher S. Adaniya
,
Phillip J. Marzette
,
K. C. King
,
S. Jeffrey Underwood
, and
John M. Lewis

Abstract

The synoptic structure of two case studies of heavy “spillover” or leeside precipitation—1–2 January 1997 and 30–31 December 2005—that resulted in Truckee River flooding are analyzed over the North Pacific beginning approximately 7 days prior to the events. Several sequential cyclone-scale systems are tracked across the North Pacific, culminating in the strengthening and elongation of a polar jet stream’s deep exit region over northern California and Nevada. These extratropical cyclones separate extremely cold air from Siberia from an active intertropical convergence zone with broad mesoscale convective systems and tropical cyclones. The development of moisture surges resulting in leeside flooding precipitation over the Sierra Nevada is coupled to adjustments within the last wave in the sequence of cyclone waves. Stage I of the process occurs as the final wave moves across the Pacific and its polar jet streak becomes very long, thus traversing much of the eastern Pacific. Stage II involves the development of a low-level return branch circulation [low-level jet (LLJ)] within the exit region of the final cyclone scale wave. Stage III is associated with the low-level jet’s convergence under the upper-level divergence within the left exit region, which results in upward vertical motions, dynamic destabilization, and the development of mesoscale convective systems (MCSs). Stage IV is forced by the latent heating and subsynoptic-scale ridging caused by each MCS, which results in a region of diabatic isallobaric accelerations downstream from the MCS-induced mesoridge. During stage IV the convectively induced accelerating flow, well to the southeast of the upper-level jet core, organizes a midlevel jet and plume of moisture or midlevel atmospheric river, which is above and frequently out of phase with (e.g., southeast of) the low-level atmospheric river described in Ralph et al. ahead of the surface cold front. Stage V occurs as the final sequential midlevel river arrives over the Sierra Nevada. It phases with the low-level river, allowing upslope and midlevel moisture advection, thus creating a highly concentrated moist plume extending from near 700 to nearly 500 hPa, which subsequently advects moisture over the terrain.

When simulations are performed without upstream convective heating, the horizontal moisture fluxes over the Sierra Nevada are reduced by ∼30%, indicating the importance of convection in organizing the midlevel atmospheric rivers. The convective heating acts to accelerate the midlevel jet flow and create the secondary atmospheric river between ∼500 and 700 hPa near the 305-K isentropic surface. This midlevel moisture surge slopes forward with height and transports warm moist air over the Sierra Nevada to typically rain shadowed regions on the lee side of the range. Both observationally generated and model-generated back trajectories confirm the importance of this convectively forced rapid lifting process over the North Pacific west of the California coast ∼12 h and ∼1200 km upstream prior to heavy leeside spillover precipitation over the Sierra Nevada.

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