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The Collaborative
Historical African Rainfall Model (CHARM)
One substantial limitation to studying rainfall in Africa
is the limited number of gauge observations available internationally.
To overcome this limitation, we have developed the Collaborative
Historical African Rainfall Model1.
The two key sources of data for CHARM are the National Center
for Environmental Prediction (NCEP) reanalysis time-series
and gridded station data. The daily estimated precipitation
fields from the reanalysis are smoothed with a specialized
spatial filter. This generates a set of 'synoptic' rainfall
fields at a resolution of 0.1 degree. The gridded monthly
precipitation fields produced by Cort Willmott (Willmott,
1994; Willmott, 1995) are then used to provide a monthly bias
correction of the daily rainfall fields. Both the GCM and
Willmott precipitation fields vary smoothly in space. Compared
to stream gauge data, they also appear to under-represent
total precipitation values in regions with significant topography.
These areas experience increased rainfall due to several compounded
effects. Orography provides a source of vertical lifting,
but can also block, channel and heat the surrounding atmosphere.
I model the first effect, lifting, but not the latter, through
the use of a single column diagnostic model. The diagnostic
model uses the terrain-gradient, surface wind vector, and
a simplified gravity wave model (Durran, 1990) to determine
the vertical velocity profile. The vertical velocity at the
surface can be approximated as (Sinclair, 1994)
Ω ≈ -ρgvs • ∇z
Where ωs
is the vertical velocity in pressure coordinates [pa/s], ρ the
density of air [kg/m3], g the acceleration due to gravity
[m/s2], vs
is the two-dimensional wind vector at the surface [m/s] and
∇z the
regional two-dimensional gradient of the terrain [m/m]. The
-ρg term arises from the hydrostatic balance between the
vertical pressure and gravitational forces within a fluid
(δp/δz = -gρ ), and translates
the vertical flux from m/s to Pa/s. The vertical velocity
profile, a parameterization of the impacts of relative humidity
and the conservation of energy and moisture are then used
to derive estimates of orographic rainfall on a 0.1 degree
grid. The scale analysis used to derive the internal gravity
wave equations2
shows that topographic gradients with characteristic lengths
of less than approximately 15 km create evanescent (imaginary)
solutions within stable atmospheric conditions. Only sinusoidal
(real ) solutions of the vertical internal wave equations
transport energy upward (Holton, 1992). Thus, when orography
enhances precipitation through forced ascent the atmospheric
response is to a relatively smooth topography. The magnitude
of these waves are determined by the terrain-induced vertical
motion at the surface (ωs),
while their frequency is a function of wind speed and the
brunt-vaisailla (buoyancy) frequency:
ωp=ωs sin(N/ν(ps-p))
Where ωp is the terrain-induced
vertical motion at pressure level p, measured in units of
Pa/s, v is the wind-speed orthogonal to the slope [m/s] and
N is the atmospheric buoyancy frequency [1/s]. ωs
is the terrain-induced vertical velocity from the equation
above in Pa/s, while ps and p are atmospheric pressure in
pascals at the surface and level at which the equation is
evaluated. Note that negative values of ωp
and ωs indicate ascending
motions since pressure diminishes with height. This equation
may be used to determine the orographic rainfall (RVDELB)
at a given location, and this rainfall may be merged with
spatially smoothed Global Climate Model rainfall (RGCM) according
to:
RCHARM=aGCM+bRVDELB
where a and b are unitless weights used to combine the GCM
and VDELB rainfall surfaces. b is determined to be 0.5, based
on hydrologic mass balance considerations, and a is estimated
from interpolated rainfall fields: a = Rinterp/RGCM.
The a parameter grids are calculated for each month over the
period 1961-1996 by constraining the average reanalysis precipitation
totals to equal the equivalent grid cell from the interpolated
GHCN rain gauge data. These a parameter grids can be used
to perform a monthly bias correction of the reanalysis precipitation
fields, a technique which has been shown to generate useful
estimates of synoptic rainfall patterns. These estimates tend
to underestimate the actual rainfall amounts in areas of Africa
with significant orography, as estimated by hydrologic models
and stream gauge data. This results from the extremely low
station data density of the Global Historical Climate Network,
and the fact that most stations follow population distributions,
which tend to be in valley bottoms. The modeling process generates
0.1 degree/daily precipitation fields for all of Africa for
the period 1961-1996. The CHARM reference below has more details,
including several validation studies.
more information
on downloading the CHARM data
References:
Funk, C., J. Michaelsen, J. Verdin, G. Artan, G. Husak, G.
Senay, H. Gadain, and T. Magadazire, 2003: The Collaborative
Historical African Rainfall Model: Description and Evaluation.
International Journal of Climatology, 23, 47-66
CHARM_IJOC_article.pdf
Funk, C. and J. Michaelsen, 2003: A simplified diagnostic
model of orographic rainfall for enhancing satellite-based
rainfall estimates in data poor regions. Journal of Applied
Meteorology, submitted, 22.
VDELB.pdf
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