SPATIOTEMPORAL STATIONARITY OF THE MEAN RAINFALL

1
SPATIO-TEMPORAL STATIONARITY OF THE MEAN RAINFALL

• Armand NZEUKOU
• University of Dschang Cameroon
• Henri SAUVAGEOT
• University of Toulouse III France

2
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)

3
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

It is possible to observe sea-land differences in
the distribution of the rain field
characteristics ?
Computed over 39 years (1951-1989) by LHote and
Mahé (1996). The dots are the synoptic
observational station managed by national
meteorological staff
4
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 lAtmosphère
  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
5
Parameters to characterize precipitation

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

6
Distribution of the annual mean 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

Area average of the cumulative rainfall (H)

• Very strong sea-land and north-south gradient.
• The differences are 112 and 69 respectively

The scale is in millimeter
7
Distribution of the annual mean rain duration
( T )
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 average

The scale is in days
8
Probability density function of the rain rate
observed P(R)
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
9
Distribution of the time-average rain rate ?R
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

The scale is in millimeter per hour
10
Distribution of the standard deviation ?R of
rain rate
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

The scale is in millimeter per hour
11
Distribution of the variation coefficient
CV?R/?R
Area average of the variation coefficient (CV)

• The CV distribution is very homogeneous

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

• 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)

i.e., ?R and ?R do not differ when computed over
different data samples (e.g., Bendat and Piersol)
12
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