Interpolation of rainfall observations during extreme rainfall events in
complex mountainous terrain
Abstract
The representation of rainfall is important for hydrological modelling,
particularly for spatially distributed models. Accurate estimation of
rainfall is particularly challenging in mountainous regions where
observations are often sparse relative to the spatial variability of
rainfall, making interpolation challenging. In these regions, orographic
processes lead to complex patterns of rainfall enhancement and rain
shadow depletion. This study tests one deterministic method, Natural
Neighbour Interpolation (NNI), and two geostatistical methods, ordinary
kriging (OK) and ordinary cokriging (CK), to determine if CK improves
rainfall interpolation during three extreme rainfall events that
occurred in the north west of England. Preliminary analysis using
long-term annual average rainfall totals, including additional high
elevation rainfall observations, showed that CK with an effective
elevation index as a secondary variable performed better than NNI and OK
with an overall improvement of around 40%. Using rainfall totals for
long-term wind direction and wind speed rainfall classes, CK performance
was variable across classes but provided an improvement of approximately
15% for wind direction classes without an easterly wind component. For
15-minute timesteps during extreme rainfall events, there were
comparatively small differences between interpolation methods,
attributed to having only relatively low elevation rainfall observations
for cross-validation, providing weak constraint. Importantly,
cross-variogram estimation (that controls the strength of the
correlation between rainfall magnitude and the secondary variable)
provided differing cross-validation results when estimated for different
rainfall total periods: 15-minutes, hourly, daily and long-term.
Variograms and cross variograms estimated at a 15-minute timestep
frequency were robust for many timesteps, but were difficult to fit
automatically for others. Variograms estimated from longer periods were
more reliably estimated, but tended to have lower variance and
cross-variance and longer correlation ranges producing a smoother
interpolated rainfall field. Given the weak cross-validation constraint,
care must be taken in identifying the most appropriate method and
variogram estimation period.