DR Elizabeth M. Saunders

Saunders, E. M.

doi:10.1111/j.1601-1546.2005.00136.x

Cited by 9 publications

(8 citation statements)

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“…Since (10.34) is an exact factorization of an approximation to A, we can think of it as a rather special approximate factorization of the original coefficient matrix A. An alternative factorization (for symmetric G), related to the null space method, is the following (Saunders 2005): (10.35) where…”

Section: Approximate and Incomplete Factorization Methodsmentioning

confidence: 99%

Numerical solution of saddle point problems

Benzi¹,

Golub²,

Liesen³

2005

Acta Numerica

1,984

1,774

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Abstract. Large linear systems of saddle point type arise in a wide variety of applications throughout computational science and engineering. Due to their indefiniteness and often poor spectral properties, such linear systems represent a significant challenge for solver developers. In recent years there has been a surge of interest in saddle point problems, and numerous solution techniques have been proposed for solving this type of systems. The aim of this paper is to present and discuss a large selection of solution methods for linear systems in saddle point form, with an emphasis on iterative methods for large and sparse problems.

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Section: Approximate and Incomplete Factorization Methodsmentioning

confidence: 99%

Numerical solution of saddle point problems

Benzi¹,

Golub²,

Liesen³

2005

Acta Numerica

1,984

1,774

View full text Add to dashboard Cite

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“…Similarly sized drops have been reported in shallow cumulus clouds over Hawaii, but with cooler cloud bases (18 • C; Beard et al 1986). Saunders (1965) reported that rain in the Bahamas could develop from fractocumulus clouds that grew into tall cumulus in ∼25-35 minutes. He also noted that extreme rain rates of 100 mm h −1 had durations of only ∼1-2 minutes.…”

Section: (B) Onset and Production Of Rain By The Collision-coalescencmentioning

confidence: 99%

“…about the minimum depth to ensure rain in KWAJEX) would take only ∼5-10 minutes. Saunders (1965) reported that in the Bahamas there was not much change in rain intensity with increasing cloud depth once a cloud attained a depth of about 4 km, even if it subsequently grew to a depth of 15 km. Since clouds 4 km deep in the Bahamas are all liquid and clouds 15 km deep certainly contain ice, it appears that the presence of ice in deeper clouds contributes little to rain intensity in the Bahamas.…”

Section: (B) Onset and Production Of Rain By The Collision-coalescencmentioning

confidence: 99%

Microstructures and precipitation development in cumulus and small cumulonimbus clouds over the warm pool of the tropical Pacific Ocean

Rangno

Hobbs

2005

Quart J Royal Meteoro Soc

111

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SUMMARYIn situ airborne measurements obtained in convective clouds in the vicinity of the Marshall Islands on 15 days in July and August 1999 are used to determine the microphysical structures and precipitation-producing mechanisms in these clouds. The liquid water contents of the clouds were generally well below adiabatic values, even in newly risen turrets. This is attributed to the entrainment of ambient air and to the very efficient removal of cloud water by the collision and coalescence of drops. The formation of raindrops began when the concentration of droplets with radii >15 µm exceeded ∼3 cm −3 or, equivalently, when the effective cloud drop radius reached ∼13 µm. Clouds rained when their depth exceeded ∼1.5 km. Due to rainout, the effective radius of cloud droplets began decreasing ∼2-4 km above cloud base.Extremely high concentrations of ice particles (often >500 litre −1 ) formed very rapidly at temperatures between −4 and −10 • C. High-resolution imagery of these particles, which were primarily sheaths, needles, frozen drops and irregular ice fragments, indicates that the high concentrations of ice were initiated by the freezing of individual drops, some of which fragmented upon freezing, accompanied by ice splinter production during riming. However, for ice particles <100 µm in maximum dimension, frozen drops and ice fragments were much more numerous than columnar ice crystals, the latter being indicative of ice splinter production. Narrow (10-50 m wide) streamers of precipitation containing large (>3 mm diameter) solid and liquid particles were often encountered in growing clouds. It is proposed that the particles in these streamers grew rapidly by riming in water-rich zones and, under appropriate conditions, the ice particles produced by both drop fragmentation and riming resulted in exceptionally high localized concentrations of ice. Convective clouds consisting entirely of liquid water produced rain rates that were similar to those from deep convective clouds containing ice.Since the concentration of drizzle and raindrops within a few kilometres of cloud base was highly correlated with cloud depth, and therefore cloud top temperature, the concentration of raindrops in cumulus and cumulonimbus clouds over the warm pool of the tropical Pacific Ocean can be inferred from satellite measurements of cloud top temperatures.

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“…In the following research design process from Saunders et al (2009), we chose the philosophical stance of critical realism as the ontological stance for the study. This stance combines the perspective of an objective and measurable reality with the assumption that people's interpretation of this reality is situation-dependent and subjective.…”

Section: Methodsmentioning

confidence: 99%