Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model

Deborah E. Ross University of Montana Department of Physics and Astronomy Condensation-Induced Windsa supplemental theorem to the traditional thermal wind model

Overview • Basic Meteorological Assumptions • Traditional Wind Model • Condensation Induced Winds • Derivation • Experimental Evidence • Greater Implications • Future Research

Weather vs Climate

Basic Meteorological Assumptions: • Hydrostatic Equilibrium • Ideal Gas Law • Adiabatic Expansion

Hydrostatic Equilibrium

Ideal Gas Law

Adiabatic Expansion Increase in volume without heat flow in or out of the volume (mb) apollo.lsc.vsc.edu Height Distance (m)

Traditional Wind Model • Solar Heating Causes Winds. • Wind is caused by differences in pressure resulting from differential heating of the earth’s surface.

Pressure and Temperature http://www.physicalgeography.net/fundamentals/7o.html

Geostrophic Wind ww2010.atmos.uiuc.edu

Thermal Wind Equation vg – Geostrophic wind vT – Thermal wind f – Coriolis parameter R – Ideal gas law constant

Equations of State for Moist Air Moist air as a whole Water Vapor Dry Air P - pressure N – molar density R – molar gas constant T – absolute temperature

Relative Molar Density of Water Vapor The process of condensation in the rising air should be reflected through the changes in:

Molar rate of condensation per unit volume: (1) - velocity vector directed along the temperature gradient toward the lower temperature - vertical velocity - horizontal velocity vertical condensation rate Gravitational expansion Horizontal expansion

Coordinate System w0,u0 is considered to be the isothermal plane whereas w,u is the horizontal plane.

Stationary Continuity Equation (2) • If we consider: (3) • And the conservation of mass for dry air: (4)

We can conclude that: • If we assume an isothermal plane, molar density does not change. (5) (6)

We can combine (1) and (5) with a substitution from (6) to obtain: (7) (1) (5) (6)

Compact Form: Using the definition for : (8) (9)

Hydrostatic Equilibrium • Adiabatic ascent of moist saturated air • The only phase transition will be condensation in the vertical direction. • Looking strictly at isothermal horizontal plane:

Adiabatic Ascent Parcel will not rise in a vertically isothermal atmosphere

Adiabatic ascent with a temperature gradient applied in the vertical direction.

Cylindrical Transformation: Using change of coordinates:

Cylindrical Coordinates u(r) - radial velocity w(r) – vertical velocity v(r) – tangential velocity

U - The velocity of hurricane movement as a whole also known as translation speed.

Theoretical radial and tangential velocity vs category 5 data set o – Data at different levels from twelve observed category 5 hurricanes.  - Median values of data sets. Data Analysis from Makarieva and Gorshkov

Theoretical Pressure profile vs Holland’s profile Theoretical values for pressure vs Holland’s profile values (empirical).

Forestry and Precipitation • “The biotic pump is a mechanism in which natural forests create and control ocean-to-land winds, bringing moisture to all terrestrial life.” • -Gorshkov and Makarieva 2012

Future Research • Add a condensation component from the biotic pump theory to a climate model.

Acknowledgements • Jennifer Fowler – Mentor and all around awesome lady. • Makarieva and Gorshkov – Theory Authors. • Alex Bulmahn • MSGC (Montana Space Grant Consortium) • University of Montana Physics and Astronomy Department

Condensation- Induced Winds a supplemental theorem to the traditional thermal wind model