Geostatistical Mapping of Mountain Precipitation

Incorporating Auto-searched Effects of Terrain and Climatic Characteristics

Huade Guan, John L. Wilson, Oleg Makhnin

New Mexico Institute of Mining and Technology

American Meteorological Society 85th Annual Meeting San Diego, Jan. 11, 2005

Why use gauge data for precipitation mapping in mountains?

• Problems with NEXRAD– Beam blockage– Snow estimation– 4km pixel size

NEXRAD rainfallNew Mexico, July 1999

From Hongjie Xie, 2004

Four types of mapping approaches

Information incorporated

Spatial covariance

No Yes

Physical process

No Theissen polygon, & inverse square distance

Kriging

Yes Regression,e.g., P-Z

Cokriging (P-Z)

(examples)

Cokriging (P-Z)& De-trended

residual kriging

today

Physical process (1)Orographic effects on precip.

P (low Z) < P( high Z)

T↓wind

T↑Elevation (Z)

P (windward) > P( leeward)

Orographic lifting, & hindrance Reduction in virga effect

P (low Z) < P( high Z)

We use cos (α-ω) toapproximate terrain aspect effects

wind direction:ω

terrain aspect: α

terrain aspect

Physical process (2)Atmospheric effects on precipitationHow does this heterogeneous atmospheric moisture distribution (or gradient in atmospheric moisture) influence precipitation?

We use geographic coordinates (Longitude or X, and Latitude or Y)to capture the effect of gradient in atmospheric moisture on precipitation

GOES East 4-km, infrared imagery 2001.05.04

Study area

Auto-search orographic and atmospheric effects

)cos(43210 bZbYbXbbPgradient in moist., elevation, aspect & moist. flux direct.

Data: Gauge precip: X, Y, P; Elev. DEM: X, Y, Z, ;

Regression:

But what about moisture flux direction, ?

aspe

ctm

oist

. flu

x di

r.

64

54

sincos

:sinsincoscos)cos(

bbbb

Let

Auto-search orographic and atmospheric effects

sincos 653210 bbZbYbXbbP where b5=b4 cosω, and b6=b4 sinω, implicitly contain the moisture flux direction. And b1 and b2 include the information of gradient in atmospheric moisture.

Regression turns to:

For example, if b5 >0 and b6 >0, ω= atan (b6/b5)

Similarly, if b1 >0 and b2 >0, gradient in atmospheric moisture, or the wetter direction = atan (b1/b2)

ASOADeKAuto-Searched Orographic and Atmospheric effects De-trended Kriging

• Auto-determine moisture gradient, elevation, & moisture direction effects via regressions Included in b0, b1, b2, b3, b5, and b6.

• Construct regression map from DEM• Find residual at each gauge• Generate residual (or de-trended) map by

kriging• Construct the final precipitation map

Regression map + residual map

Study areas

1930

1940

1950

1960

1970

1980

1990

2000

2010

0 10 20 30 40 50 60 70 80

Weather stations

Year

0

50

100

150

200

250

300

350

1 2 3 4 5 6 7 8 9 10 11 12

month

MS

E

PZ: P=b0+b3*ZPZA: P=b0+b3*Z+b5*cosa+b6*sinaPZAXY: P=b0+b1*X+b2*Y+b3*Z+b5*cosa+b6*sina

ASOADeK regression improves estimates

aspect + moisture flux direction

moisture gradient

M

Moisture flux

direction1

1 2132 1983 1864 1805 1746 1367 1568 1729 172

10 18211 18012 191

ASOADeK inferred moisture flux directions

January April July November

Winter: SouthwesterlySummer: Southeasterly

Two weather patterns in Summer• Southwesterly moisture

flux related North American Monsoon(picture to the right)

• Easterly moisture flux

ASOADeK: Southeasterly

From NOAA

Mixture of the two may give apparent southeasterly moisture flux as inferred from ASOADeK

Weather pattern related to heaviest winter precipitation

Southwesterly moisture flux at the study area,

ASOADeK:Southwesterly

From Sellers and Hill, 1974

MMoisture gradient

1 2982 2953 2794 605 866 1217 1348 1459 15410 19511 28112 273

ASOADeK inferred gradient in atm. moisture

ASOADeK regression vs. PRISM

• Model estimates from both models v. measured values

• Scatter plots and fits (R2) – For three months: Feb, May & Aug.

• ASOADek regression only! – No residual kriging

horizontal axis: observation values

ASOADeK vs. PRISM

• Precipitation maps for both models, and

• QQ plots,

• for same three months: Feb, May & Aug.

• ASOADek regression plus residual map.

For ASOADeK let’s now include the residual map

ASOADeK estimates vs. PRISM

Cross validation results:

ASOADeK gives better

estimatesthan

kriging &cokriging

Conclusions• ASOADeK detects regional climate settings

using only precip. gauge data in mountainous terrain.

• ASOADeK vs. PRISM– Precipitation maps: ASOADeK ≈ PRISM– ASOADeK product has higher spatial resolution

• ASOADeK vs. other geostat. approaches– Precipitation estimates improved in comparison

with krigng and co-kriging.

Future work• Further testing ASOADeK auto-searching

capacity– Event cases– Other geographic regions

• Applications & Extensions of ASOADeK – Mapping Precipitation in mountainous regions– Studying ENSO/PDO effects on precipitation

distribution– Recovering NEXRAD beam-blockage shadow– Downscaling precip. products, e.g., NEXRAD

ain

Thank you！