OBJECTIVELY DETERMINED 10 DAY AFRICAN
RAINFALL ESTIMATES CREATED FOR FAMINE
EARLY WARNING SYSTEMS
Vadlamani B. Kumar
Research and Data Systems Corporation
Greenbelt, MD 20770
Phillip A. Arkin
Jamie V. Kousky
National Centers for Environmental Prediction
Climate Prediction Center
5200 Auth Road
Camp Springs, MD 20746
A technique for estimation of precipitation over Africa was developed to augment the
rainfall data available from the relatively sparse observational network of rain gauge stations over
this region. The method utilizes METEOSAT 5 satellite data, Global Telecommunication
System (GTS) rain gauge reports, model analyses of wind and relative humidity, and orography
for the computation of estimates of accumulated rainfall. Work on this project has been
performed for the United States Agency for International Development (USAID), Famine Early
Warning System (FEWS) to assist in drought monitoring efforts for the African continent.
Primarily due to a lack of geographically representative surface observations for the entire
continent, rain gauge reports alone are inadequate for accumulated precipitation estimates.
While numerical models produce temporally and geographically high resolution forecasts, the
precipitation forecasts are ineffective for use in making precipitation estimates due to the
inadequate parameterizations of physical processes involving moisture. Satellite derived rainfall
estimates are uniformly distributed and relatively skillful, however biases in the estimates
indicate further improvements are necessary. The approach followed for this project combines
the uniformly distributed estimates yielded from remote sensing with the rain gauge data in order
to eliminate the biases in the estimates.
A preliminary estimate of accumulated precipitation is made based on the GOES
Precipitation Index (GPI), an algorithm developed by Arkin and Meisner (1987). The GPI uses
the duration of cold cloud tops over a region for the determination of accumulated rainfall (3 mm
of precipitation for each hour that cloud top temperatures are measured to be less than 235oK).
The GPI estimate is corrected using a bias field that is calculated by incorporating the GTS
observational data and fitting the biases to a grid using optimal interpolation producing an
estimate of convective rainfall. Over regions in which precipitation is due to orographic lifting
and the clouds are relatively warm, an additional procedure is used which incorporates the local
terrain features with numerical model analyses of meteorological parameters. This process for
warm cloud precipitation estimation takes into account surface wind direction, relative humidity,
and terrain. The combined technique incorporates rainfall from both the convective and
stratiform cloud types producing a final estimate of total accumulated precipitation.
Software development, data acquisition, data processing and operational product
generation are performed at the Climate Prediction Center (CPC), a component of the National
Centers for Environmental Prediction (NCEP). This document describes: the process of data
collection, the method of GPI algorithm adjustment for inclusion of GTS rain gauge data in
estimating cold cloud precipitation, the dot product technique for estimating warm cloud
precipitation, an evaluation of the skill of the 10-day total precipitation estimates, error estimates,
and the resulting operational products made available from the CPC.
The GPI technique was developed primarily to estimate rainfall over tropical regions of
the globe where more conventional surface observations are unavailable. It has been found that
as compared to rain gauge reports, the GPI technique generally overestimates precipitation falling
over land (Arkin and Ardanuy 1989), while over tropical oceans the bias is near zero (Xie 1995).
Bias computations made as a part of the operational precipitation estimates during 1995 indicate
that the GPI algorithm generally underestimates rainfall over the coastal and mountainous
regions of Africa. Recent work at the CPC for the African continent has led to the development
of a procedure that removes biases from the GPI by computing differences from the accumulated
precipitation determined from rain gauge reports and the GPI estimate.
These precipitation estimates are performed for climatological purposes, with estimates
made for 10-day periods, a standard period defined by FEWS for drought monitoring. The
month is divided into 3 periods; the first includes precipitation for days 1 to 10, the second for
days 11 to 20, and the third which includes all remaining days in the month (which varies from 8
to 11 days in length). For each period, two separate rainfall estimates, adjusted to rain gauge
reports, are prepared; one for the cold cloud precipitation only, and the second for the combined
warm and cold cloud precipitation.
Geostationary Satellite data is utilized for the determination of cloud top temperature.
METEOSAT 5 thermal Infra Red (IR) digital data at 5 km pixel resolution is accessed every 30
minutes and then reformatted and converted to a geographic grid with a 0.1o resolution. This grid
is 751x601 points which begins with point 1,1 at 20oW, 40oS and ends at point 751,601 at 55oE,
20oN. A horizontal resolution of 0.1o was chosen for the estimate computations to correspond
with the absolute positioning error for the satellite of approximately 10 km. Arrays are used to
accumulate the occurrences of cloud top temperatures below temperatures of 235oK and 275oK.
Rain gauge reports transmitted via the GTS are received every 6 hours are utilized in the
CPC Climate Assessment Data Base (CADB), for monitoring of climate anomalies (Finger
1985). Automated quality control of these GTS observations within the CADB is done prior to
the processing of precipitation estimates (Thomas 1983). These values are then accumulated for
each 24 hour period and processed for each 10-day period. Although the total number of station
reports received varies daily, the number of stations reporting observations for each 10-day
estimation period is approximately 760.
Model analyses of surface wind and surface relative humidity are acquired from the 1o
horizontal resolution Environmental Modeling Center (EMC) Global Data Assimilation System
(GDAS). These data are obtained for the .9950 sigma level for the 00, 06, 12, and 18 UTC
analyses. The .9950 sigma level wind and relative humidity data are interpolated to a 0.1o
horizontal resolution grid using a bivariate interpolation. Here sigma is an independent vertical
coordinate defined to be the ratio of the pressure to the surface pressure, ranging from one at the
surface of the earth to zero at the top of the atmosphere. For the GDAS the .9950 sigma level is
the lowest model level available, corresponding to approximately 80 meters above the earth's
Estimation of Cold Cloud Precipitation
The first step in the process of cold cloud precipitation estimation is the computation of
an approximate rainfall estimate using the GPI algorithm. An empirical adjustment using
statistical estimation is used to correct this GPI estimate, by fitting the GPI estimates to rain
gauge data. The process involves computing the differences between the gauge rainfall amounts
and the GPI precipitation estimate, then computing a gridded bias field via an optimum
interpolation (OI) scheme. Minimization of a cost function is the primary OI method used to
produce a gridded field of precipitation estimates (Thacker, 1988).
Assuming data points exist in each grid square, the GPI estimate zi,j , and d , the rain gauge values at each observation site , are compared at each grid point (xi,yj). The output field m , the precipitation estimate, is defined by the bilinear interpolation:
The resultant grid variables are then found by minimizing the cost function:
For cases in which no data points lie within a grid square, a two dimensional least squares surface is fit, using second order polynomials to complete the bias grid field. For grid points in the proximity of rain gauges, weights in the optimum interpolation scheme are also based upon relationships derived from the computation of structure functions (Kruskal 1978).
The spatial structure of the data is determined by calculating a structure function, or semi-variogram, (Clark 1979) which graphically depicts the mean square lagged difference of the data. This structure function describes the expected differences in values of accumulated rainfall with distance. Initially the structure function weights are used to obtain a first estimate at each grid point, and the least squares minimization of cost functions is then applied in an iterative process to reduce the error, where error is defined as the difference between the initial estimates and the rain gauge
The structure function relationships indicate that model corrections to the rainfall estimate
bias can be made to improve the skill (defined here as the accuracy of the precipitation estimate) up
to a distance of approximately 4 lags, or 2.0o. The structure function curve fit for all the data points
was found to have a standard deviation of 19.4 mm. The structure functions for the precipitation and
distance relationship for the Southern Hemisphere display a reversed seasonal relationship.
The weights used in the current operational OI scheme for the regions in proximity to the rain
gauge reports are based upon the structure relationship for the Northern Hemisphere rainy season.
This was done in order to maximize the skill of the model during the season of significance, the wet
season. For grid points not in proximity to rain gauge reports, the weights determined by reduction
of cost functions are utilized to obtain the estimate field. For simplification, at the present time this
structure function relationship is assumed to be true for the entire year and over the entire continent
of Africa. (Note: Further research to investigate the seasonal variation of the structure functions will
be conducted in order to determine if a more appropriate relationship for estimating precipitation
over various geographical regions and seasons can be obtained.)
Estimation of Orographic Precipitation
The process used in the estimation of precipitation from warm cloud sources attempts to quantify the precipitation resulting from condensation of moist air masses due to vertical lift during favorable low-level wind conditions. Precipitation of this type can not be estimated using a technique such as the GPI algorithm, which relies on the presence of cold convective cloud sources. However, it is associated with cloud that can be distinguished from the surface (in relatively warm regions), and so an estimate may be possible if ancillary data are used.
Over regions in which warm cloud (top temperatures between 275o-235oK) are present and the low level wind direction is favorable for orographic lifting, the rainfall rate is estimated utilizing a procedure which combines the relative humidity, wind direction and the terrain slope. Wind vectors and relative humidity from the analyses of the EMC GDAS for the 00, 06, 12, and 18 UTC are used in computing the dot product. The slope of the terrain is computed with a finite difference method using a .1 degree horizontal resolution.
The dot product of the terrain slope and wind is computed at intervals of every half hour, although the wind is assumed to be a constant value throughout the 6 hour period. The scalar product of the surface wind vector (u(x,y), v(x,y)) and the horizontal gradient of orography grad[h(x,y)] is defined as follows:
These partial derivatives are approximated by the finite differences centered at the grid points. The dot product values are then interpolated to a grid with the same resolution as the METEOSAT data. To incorporate the orographic lift of low level moisture, the dot product is then multiplied by the analyzed surface relative humidity. Every half hour these multiples of the dot product multiplied by the relative humidity values are stored for those grid points over which the cloud top temperatures obtained from METEOSAT 5 IR data range from 235oK to 275oK. These dot product values are summed for the period and then converted to a rainfall estimate with the use of a calibration from rain gauge reports.
Using a two month set of rain gauge data for sites over which there was no cold cloud duration, and precipitation was entirely orographic, calibration of the estimates provided by the dot product technique was done. The present calibration is based upon data acquired during the period May 20-July 19, 1995. This relationship is applied uniformly over the continent without regard to geographic location of the sites utilized for the calibration. Although a change to the calibration equations would result in a modification of the relationship used to convert the dot product/relative humidity product to rainfall, further calibration is planned to improve the relationship between the orographic lift and the resultant precipitation estimates. Investigation into the seasonal variability of the calibration will be made in future work.
Evaluation of GPI Algorithm
In order to assess the skill of the GPI algorithm for total precipitation estimates, the estimates for a specific 10-day period were compared to the GTS rain gauge reports received for that period. The results for the second 10-day period in October 1995, show that the standard deviation of the GPI estimate was equal to or greater than the measured rainfall amount, for amounts up to 60 mm. Here the standard error, or standard deviation is defined as:
Where the differences between the GPI estimate and the rain gauge report were computed at grid points j, corresponding to the geographic location of the rain gauge report. The results for this specific period indicate that for rainfall amounts of less than 60 mm, the magnitude of the estimate error is equal to the magnitude of the estimates. In contrast, for rainfall amounts of 60 mm and greater, the magnitude of the error is less than the estimate. Due to the relatively few actual rain gauge reports of precipitation with amounts greater than 60 mm, a true assessment of estimation skill can not be made. For this specific 10-day period, these results indicate that the GPI algorithm produces skillful estimates for rainfall amounts in excess of 80 mm. Although the error in the GPI estimates for this specific 10-day period is relatively large in comparison to the estimate, the correlation of the GPI estimate with the rain gauge data is relatively high. The correlation between the 456 rain gauge reports available during the period from 21-31 October 1995, and the GPI estimate was .67.
A true assessment of the geographic and seasonal variation in the skill of the GPI algorithm for precipitation estimates has not yet been done, however for this particular 10-day period, the standard deviation of the GPI estimates indicates the necessity of the use of an additional data source.
Evaluation of Interpolation Error
In order to assess the maximum possible interpolation distance between GTS reports to produce skillful estimates, variances were computed as a function of station separation. For the first 10-day period in July, the depiction of the Standard Deviation (error) as a function of distance between the rain gauges indicates error increases rapidly over the distances from 0 to 100 km. Up to a distance of 50 km, the error increases almost linearly. Beyond a distance of 100 km, there is an almost uniform standard deviation of 50 mm. This implies that there is large variability in rainfall with distance, and indicates the necessity of using additional data sources in addition to the GTS rain gauge reports.
Evaluation of CPC Estimation Technique
Utilizing a set of entirely independent precipitation data provided by Felix Lee of the USAID/FEWS project, an evaluation of the precipitation estimates made operationally was done for the Sahel region of Africa. This evaluation was done for the results of the combined process which produces estimates of rainfall accumulation from both cold and warm cloud sources.
The field data used in the evaluation was collected at sites other than at the WMO stations used in the operational production of the estimates. Data from 180 stations, yielding 1882 observations from the countries of Mali, Niger, and Chad were used in the assessment of the estimation technique. In order to examine the skill of the combined technique, only the period from June 1 to September 31 was utilized in the computation of the statistics presented here since the dot product/relative humidity algorithm was only implemented operationally June 1, 1995.
To allow for an examination of a range in the estimated skill, three separate methods of comparison were computed. The reported rain gauge amount was compared to: a) the estimation value at the nearest corner of the grid box, b) to the grid box with a value closest to that of the rain gauge value, and c) to the average of the four corners of the grid box. A comparison of the results of these three methods indicate there is very little range in the computed standard deviation for the three methods of assessment. The skill of the GPI algorithm is very similar to that of the CPC estimates for accumulated precipitation amounts in excess of 100 mm. The standard deviation of the rainfall estimates indicates that the estimates have a maximum error of approximately 40% of the measured precipitation value with a 68.3% assurance. Standard deviation of the rainfall estimates increased nearly linearly with accumulated precipitation amount for all three methods. For this same period, the correlation between 1780 points of independent field data and the accumulated precipitation estimate was .86.
A 10-day rainfall estimate is prepared operationally at the Climate Prediction Center for the USAID/FEWS Program. Cold cloud duration, computed bias, and the resulting rainfall estimates (prepared with and without the dot product/relative humidity analysis) are stored as gridded files in eight bit integer words, for both compactness and compatibility with personal computers.
Precipitation estimates are produced on the 1st, 11th, and 21st of each month. In addition to being available on this ADDs server, graphics and data for the 10-day estimates, cloud top temperature graphics and meteorological analyses of parameters for the African continent are made available to the public via the World Wide Web at the following URL:
Work done with the GPI algorithm since January of 1995 has led to the development of a model which completes a bias adjustment to the GPI estimates through inclusion of rain gauge reports, optimal interpolation weights determined from use of structure functions, optimalization of cost functions, and the dot product of the wind and orography multiplied by the relative humidity. Estimates of precipitation from this method are currently being made operationally each period for the African continent. An assessment of the model skill at providing estimates for both warm and cold cloud accumulated precipitation demonstrates relatively high accuracy for the region of North Africa. Continued work to assess the model skill for other regions of Africa will be completed upon availability of additional field data.
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