SPATIO-TEMPORAL STATIONARITY OF THE MEAN RAINFALL

Armand NZEUKOU University of Dschang Cameroon

&

Henri SAUVAGEOT University of Toulouse III France

Localization– Tropical latitude with a seaward

circulation– The Climate of the Dakar area is of

sahelian type– The rainy season is reduced to

about 3 months, from early July to late September

– Most rainfalls become weaker and then disappear when crossing the coast and moving over the nearby ocean

– A few systems grow stronger, advance over the sea, and seem eventually able to play a role in the genesis of the hurricanes of the west tropical Atlantic (Gray and Lansea, 1992)

0 ° N

1 4 ° 3 4 ' N

4 4 ° 5 2 ' N

0°30

' W

17°2

9' W

Africa

Europe

D akar

Bordeaux

Gauge-based mean annual cumulative rainfall for Senegal

- The mean annual cumulative rainfall displays a strong meridional gradient, from 300, at the latitude of Saint Louis, to 1500 mm at Cap Skirring, which is 400 km away

- As in most similar rain field representations, isohyets end at the coast. Thus the rain field characteristics over the sea are poorly documented

- In this work, we are to describe and to discuss the characteristics of the rainfall distribution in coastal area, which offer an opportunity to observe the land – sea contrast

300

400

500

600

700

800

1000

1200

16°N

12°N

18°W

16°W

1500

2000

14°W

Saint Louis

Rosso Sénégal

Kaédi

MatamLinguère

Dakar

Diourbel

Kaolack

BanjulGeorgetown

Tambacounda

Cap SkirringZiguinchor

Kolda Simenti

BissauBoloma

Bafata

Podor

MAURETANIA

SENEGAL

GUINEA

It is possible to observe sea-land differences in the distribution of the rain field characteristics ?

Computed over 39 years (1951-1989) by L’Hote and Mahé (1996). The dots are the synoptic observational station managed by national meteorological staff

Studied area and radar dataset• Land and sea areas are colored• North and south areas are half-

annular areas located north and south of the latitude of the radar between 60 and 180 km

• Dataset– The data acquisition was

performed by the staff of the Laboratoire de Physique de l’Atmosphère Siméon Fongang of the universitiy of Dakar, using a « SANAGA » acquiring system develop by Sauvageot.

– Period of observation:7 years (1993 à 1999)

– sampling interval:between 10 and 20 min

– number of scans:7407

Location and shape of the areas used to computed the averaged parameters

North

South

Sea Land

-150 -100 -50 0 50 100 150

Distance from radar [km ]

-150

-100

-50

050

100

150

Dis

tanc

e fr

om r

adar

[km

] 60 km

180 km

D akar(R adar)

Parameters to characterize precipitation

• Cumulative rainfall• Rainfall duration•Average rain rate•Standad deviation of rain rate•Variation coefficient

Distribution of the annual mean cumulative rainfall ( H )

Sea Land North

South

298 632 344 583

-200 -150 -100 -50 0 50 100 150 200

D istance from radar [km ]

-200

-150

-100

-50

0

50

100

150

200

Dis

tan

ce f

rom

ra

da

r [k

m]

0

200

400

600

800

1000

1200m m

• Very strong sea-land and north-south gradient.

• The differences are 112% and 69%

respectively

Area average of the cumulative rainfall (H)

•The surface echoes area is very asymmetrical and is mainly over the cape of Dakar.

•Screening effects are observed for azimuths 225° and 240°

The scale is in millimeter

Distribution of the annual mean rain duration ( T )

Sea Land North

South

53,4

105 56,7 97,5

-200 -150 -100 -50 0 50 100 150 200

D istance from radar [km ]

-200

-150

-100

-50

0

50

100

150

200

Dis

tan

ce f

rom

ra

da

r [k

m]

0

2

4

6

8

10

12day

Area average of the rain duration (T)

• Very strong sea-land and north-south gradient.

• The differences are 97% and 72%

respectively • The T variation is almost the same as the H

• That suggests that the rain rate can be considered constant in the area averageThe scale is in days

Probability density function of the rain rate observed P(R)

-6 -4 -2 0 2 4 60

2

4

6

8

10

12

14

ln(R)

P(%)

LandSea

-6 -4 -2 0 2 4 60

2

4

6

8

10

12

14

ln(R)

P (%)

NorthSouth

For all the R values higher than the mode of P(R), the frequency is lower over sea than over land. That suggest a convection slightly less vigorous over sea than over land

The north and south P(R) curves coincide almost exactly despite the strong gradient of the cumulative rainfall

The shape of P(R) is compatible with a lognormal distribution which is defined by two parameters, namely, the average (R) and the variance (R) of the rain rate

Distribution of the time-average rain rate R

Sea Land North

South

4,8 5,35 5,18 5,03

0.0

2.0

4.0

6.0

8.0

10.0

-200 -150 -100 -50 0 50 100 150 200

D istance from radar [km ]

-200

-150

-100

-50

0

50

100

150

200

Dis

tanc

e fr

om r

adar

[km

]

12.0mm h - 1

The scale is in millimeter per hour

Area average of the rain rate (R)

• The R distribution is mostly homogeneous except for the northwestern quater plan beyond 100 km.• The differences between sea-land and north-south are 11% and 3%, respectively

• The R is almost constant for the whole observed area, with sligthly lower values over the sea

Distribution of the standard deviation R of rain rate

-200 -150 -100 -50 0 50 100 150 200

D istance du radar [km ]

-200

-150

-100

-50

0

50

100

150

200

Dis

tanc

e du

rad

ar [k

m]

2 4

mm h - 1

0

4

8

12

16

20

Sea Land North

South

11,6

11,9 11,4 11,3

The scale is in millimeter per hour

Area average of the standard deviation (R)

• The R distribution is very homogeneous except for the northwestern quater plan beyond 100 km.

• The R is very constant for the whole observed area

Distribution of the variation coefficient CV=R/R

Sea Land North

South

2,42

2,22 2,20 2,25

0.50

1.25

2.00

2.75

3.50

4.25

-200 -150 -100 -50 0 50 100 150 200

D istance from radar (km ]

-200

-150

-100

-50

0

50

100

150

200

Dis

tan

ce f

rom

ra

dar

[km

]

5 .00

Area average of the variation coefficient (CV)

• The CV distribution is very homogeneous

• Only the knowledge of the mean rain rate enables the definition of R and P(R). It shows that the observed rain rate fields are approximately spatio-temporal stationary (or ergodic)

• The mean value is 2.27 and very close to the value proposed by Sauvageot (2.24) over large space and time samples.

i.e., R and R do not differ when computed over different data samples (e.g., Bendat and Piersol)

CONCLUSION

• The rain volume or cumulative rainfall is higher over land than over sea by 112%

• The rain duration is longer over land than over sea by 97%

• The probability density distribution of the rain rate is well represented by a lognormal function, which is determined by two parameters, the mean R and the standard deviation R

• The stability of R and R through rain fields implies the same stability for the probability density function of R or P(R).

• The rain field studied is approximately spatio-temporal stationary or ergodic and justifies the validity of P(R) as a significant rain field characteristic