title: The spatial statistical distribution for multiple rainfall intensities over Ghana
Creators: name: Israelsson, Jennifer E.
Publisher: name: University of Reading
Year: 2022

description: Accurately measuring rainfall is important in most parts of the world due to our reliance on it
for food, energy and drinking water. The seasonality and interannual variability at a daily scale
needs to be understood for our current climate in order to understand how it is changing with
global warming. However, obtaining this information for large land areas, such as the African
continent, down to the few km level instead of a regional or country levels is difficult due to the
very large number of rain gauges required. Rain gauges is the preferred measurement method
since it provides the most accurate amount for a specific location. Satellites on the other
hand can easily collect information over a whole continent, but these cannot directly measure
rainfall. It therefore needs to be calibrated against ground observations and in addition only
returns an area average estimate instead of a point estimate. An optimal observation product
would draw information from both of these sources when appropriate, but this requires a detailed understanding about the radius the rain gauge information can be extrapolated to and
the relation between the two sources of information.
This thesis aims to achieve improvements in these two areas. The first contribution is to
provide new methods for estimating the correlation distance for all rainfall intensities, information which can be used to inform about the radius a gauge measurement can be extrapolated.
The second is to provide an improved distribution function for daily rain gauge measurements
associated with satellite estimates at a 4km scale. The combination of these two can improve
the merging of information from rain gauges and satellite estimates by drawing information
from the most accurate source at each location. The application of the new methodologies are
demonstrated by applying these to a new, dense daily rain gauge data set collected over Ghana.
A non-parametric methodology for estimating the correlation distance is developed, which
can easily be adapted for a given study region. Based on comparing the observed with the
expected co-occurrence probabilities, it by design takes into account the rainfall climate for the
specific time period and rainfall intensity considered. The annual variation of the correlation
range for four intensity classes is estimated over southern Ghana, and compared with estimates
from previous studies for other west African countries.
To estimate the dependence structure in extreme values, and especially for values larger
than the ones observed, multivariate Extreme Value Theory provides the appropriate framework. A semi-parametric estimator for the coefficient of tail dependence is proposed and the
performance is evaluated in a finite sample simulation study. The extremal dependence structure for different times of the year is evaluate by applying the estimator to the daily rain gauge
data set collected over Ghana. Limitations stemming from strong seasonality and missing values are addressed.
A qualitative study for assessing the distributional fit of rain gauge measurements conditioned on a satellite rainfall estimate is performed, with the 4km satellite estimates given by the
TAMSAT data set. A skewed distribution with heavier than normal distributed tails is found
to generally be suitable.