The Lagrangian Evolution on Water Budget and Precipitation

Efficiency of Squall-Line Systems as Interacting with Terrain

Ming-Jen Yang 楊明仁, Yi-Chuan Chung 鍾宜娟, Mark Yin-Mao Wang 王尹懋

National Taiwan University

Submitted to the JAS

June 2006

A Conceptual Model for the Water Budget of Tropical Cyclone

CMPE (Cloud Microphysics Precipitation Efficiency; Huang et al. 2014):

Rainband

Water Budget

LSPE (Large-Scale Precipitation Efficiency; Sui et al. 2007; Yang et al. 2011): PE = P/[HFC + VFC]

• Use the explicit high-resolution (1-km) WRF model to simulate an idealized squall-line system crossing a bell-shape mountain and investigate

its evolution of water budget and PE.

• Common knowledge:

Motivation

Water vapor

convergence Condensation

Precipitation

efficiency

Q1: How much of rainfall enhancement

by terrain lifting?

Q2: Function of Froude number ?

When a convective system (squall line or TC) interacts with Taiwan terrain:

Three Microphysical-Process Ratios

Condensation Ratio: Deposition Ratio: Evaporation Ratio: where is the total condensation and deposition; is the cloud water condensation; is the snow deposition; is the graupel deposition; is the cloud ice deposition; is the raindrop evaporation

Initial Environmental (Mei-Yu) Sounding & Vertical Wind Profile

SL Mt.

240 km

Squall Line

Initiation

Froude Number : Fr = U/NH

H U 5 m/s 7.5m/s 10m/s 12.5m/s 15m/s

1 km 0.77 1.16 1.54 1.93 2.32

2 km 0.46 0.68 0.91 1.14 1.37

3 km 0.38 0.57 0.76 0.95 1.14

4 km 0.29 0.43 0.57 0.72 0.86

• Terrain Height (same Horizontal Wind)

No Terrain-TeU=10m/s Terrain H=1km U=10m/s

Terrain H=2km U=10m/s

Terrain H=3km U=10m/s

Terrain H=4km U=10m/s

H U 5 m/s 7.5m/s 10m/s 12.5m/s 15m/s

1km 1.54

2km 0.91

3km 0.38 0.57 0.76 0.95 1.14

4km 0.57

-60 km

-40 km

-24 km

Mature H=1km H=3km H=2km H=4km No terrain

-12 km

0 km

12 km

Windward slope H=1km H=3km H=2km H=4km No terrain

Lee side

24 km

40 km

60 km

H=1km H=3km H=2km H=4km No terrain

H U 5 m/s 7.5m/s 10m/s 12.5m/s 15m/s

1km 1.54

2km 0.91

3km 0.38 0.57 0.76 0.95 1.14

4km 0.57

• Horizontal Wind (same Terrain Height)

Terrain H=3km U = 2.5 m/sU=5m/s

Terrain H=3km U=7.5m/s

Terrain H=3km U=10m/s

Terrain H=3km U=12.5m/s

Terrain H=3km U=15m/s

1.5 2 2.5 3

-60 km

-40 km

-24 km

U=5m/s U=10m/s U=7.5m/s U=12.5m/s U=15m/s Mature

-12 km

0 km

U=5m/s

12 km

U=10m/s U=7.5m/s U=15m/s U=12.5m/s Windward slope

U=5m/s U=10m/s U=7.5m/s U=15m/s U=12.5m/s

11hr

Lee side

24 km

40 km

60 km

H U 5 m/s 7.5m/s 10m/s 12.5m/s 15m/s

1km 0.77 1.16 1.54 1.93 2.32

2km 0.46 0.68 0.91 1.14 1.37

3km 0.38 0.57 0.76 0.95 1.14

4km 0.29 0.43 0.57 0.72 0.86

• Same Froude Number with different combination of U and H Froude number~0.57 [ H=3km U= 7.5 m/s vs. H=4km U=10m/s ] Froude number~0.7 [ H=1km U= 5 m/s vs. H=3km U=10m/s ] Froude number~1.14 [ H=2km U=12.5m/s vs. H=3km U=15m/s ]

∆ HFCv (109 kg/s) as a function of U and H

%

H vs. U 5 m s-1

7.5 m s-1

10 m s-1

12.5 m s-1

15 m s-1

1 km 3.01 5.81 0.90 1.46 –3.66

2 km 1.92 12.57 9.54 6.01 2.65

3 km 6.05 10.41 11.53 7.54 6.31

4 km 8.25 8.99 6.69 9.14 6.90

%

H vs. U 5 m s-1

7.5 m s-1

10 m s-1

12.5 m s-1

15 m s-1

1 km 4.25 7.76 0.81 3.59 –6.52

2 km 1.64 11.64 6.27 5.00 3.09

3 km 3.70 9.66 10.41 9.15 5.47

4 km 5.58 9.60 7.02 8.58 3.59

∆ COND (109 kg/s) as a function of U and H

%

H vs. U 5 m s-1

7.5 m s-1

10 m s-1

12.5 m s-1

15 m s-1

1 km 5.19 4.77 –0.85 3.48 –3.87

2 km 2.49 7.84 3.63 3.44 1.92

3 km 3.30 6.80 7.82 6.67 4.05

4 km 5.29 8.04 3.30 7.37 2.99

∆ P (109 kg/s) as a function of U and H

∆ PE as a function of U and H

%

H vs. U 5 m s-1

7.5 m s-1

10 m s-1

12.5 m s-1

15 m s-1

1 km 7.74 % 4.76 % 1.45 % 2.73 % –1.22 %

2 km 5.77 % 10.64 % 10.41 % 6.09 % 4.31 %

3 km 8.62 % 8.64 % 13.77 % 9.36 % 7.94 %

4 km 8.33 % 13.22 % 6.97 % 10.58 % 8.15 %

A Conceptual Model for the PE and Water Budget Evolution of

a Squall-Line MCS interacting with terrain

Conclusions • For a squall-line MCS moving across a bell-shape mountain, horizontal vapor

flux convergence (HFC) first increases, then condensation and accretion

increase, and then surface precipitation (and PE) increases on the windward

side. The reverse trend is found on the lee side.

• The Lagrangian evolution of major cells within the sqaull-line MCS shows

that PE and CR are increased on the windward slope but decreased on the lee

side; the opposite tendency is found for the DR and ER, similar to those

within outer rainbands of Typhoon Morakot (Huang et al. 2014).

• For orographic precipitation regime under the same Froude number, different

combination of terrain height and mean flow speed has different response of

rainfall enhancement (suppression) on windward (lee) side.

• For the same terrain height, there is an optimal environmental flow speed to

produce the maximum rainfall enhancement; similarly, for the same

environmental flow speed, there is an optimal terrain height to produce the

maximum rainfall enhancement.

Thank you for the attention!