Solar Radiation At the Top of the Atmosphere

When sun directly overhead, amount of solar radiation received is:

Q = S (d/d)2

– Where d – mean distance from the sun

– d – distance from sun on particular day

up

Sun

Zenith Angle

When sun is at some other zenith angle, Z (angular distance of sun from local vertical), how much solar radiation is received?

As- Area perpendicular to Sun Ap- Area perpendicular to local vertical Qs As = Qp Ap ; As = Ap cos Z

Qp = S (d/d)2 cos Z Z=0 cos Z = 1; Z=45 cos Z= .71 Z=60 cos Z = .5; Z=90 cos Z= 0 As sun becomes lower on horizon, amount of solar

energy decreases per unit area

up

Z

Sun

As

Ap

Z

Zenith Angle

Zenith angle depends on:– latitude (north +, south -) – time of year. Solar declination angle, - angular distance of the sun

north (+) or south (-) of the equator• = 23.5o on June 21 Summer Solstice• = -23.5o on Dec 22 Winter Solstice• = 0o on Sept 23 (Autumnal Equinox) and March 20 (Vernal Equinox)

– Time of day. Hour angle, h, is 0 at solar noon, when sun is directly north or south of observation point

• h increases by 15 for every hour before or after solar noon• h = -90o at 0600 LT and h = 90o at 1800 LT

Zenith Angle

cos Z = sin sin + cos cos cos h Special cases:

– Solar noon: cos h = 1. Z = – On June 21, sun directly overhead at 23.5oN• On the same day at 40oN, Z = 40 – 23.5o = 17.5o

• At 90oN, Z = 67.5o

Zenith Angle cos Z = sin sin + cos cos cos h Special cases:

At sunrise or sunset, cos Z = 0, h = H = half-day length Cos H = - tan tan At the equator, tan so H = 90o which is 6 hours On the equinoxes, tan = 0 so H = 90o or 6 hours Latitude of polar night (H=0), 90o - |in winter

hemisphere

Azimuth Angle

Azimuth angle, a, angular distance of the sun from due south

At sunrise and sunset, cos a = - sin / cos At the equator, cos = 1, azimuth angle will be most nearly due

east. a = 90 + .On the equinoxes, the sun will rise/set due east/west. At the summer solstice, a = 113.5o

As the latitude increases, the denominator decreases, and the azimuth of sunrise/sunset departs more from due east/west

Maximum Temperatures: Monday, April 15, 2002

Tax Day Storm:

April 15, 2002

Tax-Day Storm (15 April 2002):

• Extensive damage ($4M+) from high winds > 35 m / s

• Record lowest SLP (982mb) at Salt Lake City (SLC)

• Ushered in an extended period of cold/wet weather

• 5-10 year event

• Max temperature change with cold front 16 C / hr

• Prefrontal blowing dust visibility < 1 km, closed roads,

• Rained mud, brownish/orange-colored snow

(J. Shafer)

Todd Foisy. April 15, 2002

Tax Day Storm:April 15, 2002

Bagley. Salt Lake Tribune

Maximum Sustained Wind Speed (mph)

April 14-15, 2002 WBB

2 km away

~1930 UTCJ. Shafer

Limited visibility due to blowing dust

Initial Development:

•Upper-level system moved over a preexisting temperature gradient

1200 UTC, 1500-m pressures = 2mb

1500 UTC

500 kmJ. Shafer

Rapid development during daytime…

1800 UTC 2100 UTC

J. Shafer

Low track and strength

L15z

L18z

L21z

L00z

Hours from 0000 UTC 15 April

J. Shafer

14mb/9hr

Strong cold front over N. UT

WNW, gusting to 48 knots

SSE, gusting to 83 knots

25 km

2130 UTC

Strongest Baroclinity ~20 C / 100 km

J. Shafer

Closer inspection of cyclogenesis/frontogenesis:

1500 UTC

700mb: Temp (2C) and winds

1800 UTC2100 UTC

Dry slot

1800 UTC2100 UTC

Precip mostly postfrontal – N. UT

J. Shafer

Relative humidity gradient with front

Adas RH 2200 UTC

fropa

• Front was stronger where rh gradient was stronger

J. Shafer

• Highest winds correlate well with daytime heating or deep boundary layer

9 PM

11AM

Max gust versus time of day

Characteristics of the damaging winds:

> 25 m/s> 30 m/s

Coverage

•Mainly prefrontal

J. Shafer

Basic frontal dynamics – frontogenesis/lysis

Consider a zonally oriented front with a meridional temperature gradient

Frontogenesis would occur in this case depending on the interaction of:

x

y TT+TT+2T

Differentialdiabatic

heating/cooling

Cross-frontalconfluence Tilting+ +

Basic frontal dynamics – frontogenesis/lysis

Differential heating/cooling: Horizontal gradients in heating/cooling strengthen or weaken the temperature gradient

x

y

T

T+T

T+2T

Basic frontal dynamics – frontogenesis/lysis

Differential heating/cooling: Horizontal gradients in heating/cooling strengthen or weaken the temperature gradient

x

y

T

T+T

T+2T

T+3T

Frontogenesis!

Basic frontal dynamics – frontogenesis/lysis

Cross-frontal confluence: Horizontal winds (deformation) act to increase the horizontal temperature gradient

x

y

T

T+T

T+2T

Basic frontal dynamics – frontogenesis/lysis

Cross-frontal confluence: Horizontal winds (deformation) act to increase the horizontal temperature gradient

x

y

T-T

T

T+T

T+2T

Frontogenesis!

Basic frontal dynamics – frontogenesis/lysis

Tilting: Vertical motion pattern acts to “tilt” a vertically oriented temperature gradient into the horizontal

y

z

T

T-T

T-2T

AdiabaticWarming

AdiabaticCooling

Basic frontal dynamics – frontogenesis/lysis

Adiabatic warming and cooling leads to horizontal temperature contrast

y

z

T

T- T

T-2T

Frontogenesis!

How does orography affect fronts?

Movement • Low-level flow blocking and channeling may retard or accelerate

a front, resulting in a distortion of its “shape”

Frontogenesis/frontolysis• Terrain-induced horizontal flow field may contribute to

frontogenesis or frontolysis • Terrain-induced vertical motion pattern (and associated

adiabatic warming and cooling) may contribute to frontogenesis or frontolysis

Vertical structure• Low-level blocking may act to decouple surface-based and

upper-level portions of front• In some cases, entire lower portion of a front may not be able to

surmount a mountain ridge or range, leaving only upper-level front

Orographic impacts on frontal movement

“The mountain-induced flow advects and distorts a front” (Egger and Hoinka 1992)

Examples– Pre-frontal downslope (Foehn) and low-level blocking of the

post-frontal wind can retard the progression of a front on the windward side of a mountain range

– A mountain-induced anticyclone can act to rotate a front anticyclonically upwind of a mountain range

– Terrain-channeled flow along a valley, plain, or gap can produce acceleration of a front

Early examples of frontal deformation/distortion

Bjerknes and Solberg (1922): Describe how mountains can retard a warm front, resulting in development of “warm-core seclusion” and secondary cyclogenesis

Nor

way

Nor

way

Nor

way

Seclusion

Early examples of frontal deformation/distortion

Bergeron (1928, available in Godske et al. 1957): Orographic distortion of a cold front by topography of Europe

• Frontal retardation windward of Alps• Frontal acceleration in Rhone Gap between Alps/Pyrenees

(Mistral), as well as east of Alps

Terrain channeling

Post-frontal flow becomes oriented along valley axis

Cold-air is transported rapidly up valleySteenburgh and Blazek (2001)

Smith (1986)

Terrain channeling

Terrain-parallel jet may develop in post-frontal environment Contributes to development of frontal nose

Steenburgh and Blazek (2001)

Orographic impacts on frontogenesis/frontolysis

Horizontal winds generally frontogenetical for whole case, but flow splitting around Olympics enhances frontogenesis as front initially approaches windward slopes

Frontolysis over mid and high elevation slopes where tilting generally contributes to frontolysis

Summary

Topography can distort the structure of a low-level cold front in several ways

• Fronts can be retarded by pre-frontal downslope and blocking of the post-frontal airmass windward of the topography

• Fronts may rotate anticyclonically due to development of mountain anticyclone

• Along-valley or gap winds may accelerate fronts through lowland regions

• Low-level and upper-level portions of a front may become decoupled

Mountain-induced horizontal winds and vertical motion can result in frontogenesis or frontolysis

Frontal analysis in complex terrain is difficult, but is being improved over western U.S. by MesoWest

Wave above convection streets

WMO (1993)Wind speed component normal to street axis should exhibit shear greaterthan 3 m/s per 1000 m both above and below the inversion. Then, streetsact line a line of mountain ranges and a wave develops above the street.

Monthly frequency of lee wave clouds in Europe

After Cruette (1973)

Wave climatology of W Europe under NWly flow

After Cruette (1973)

Numbers indicate frequency of observance; orientation and areal extension is as shown; from satellite picturesfrom 1966-1968.

Position of wave in lee of Sierra Nevadas

WMO (1993)