# Comparing models with observations

 By Dr. Sarah Dance (University of Reading) 20th August 2014

Weather and river flood forecasts are based on the output from a numerical computer model. Such models are built from a mathematical description of physical laws that govern the behaviour of the atmosphere or the water in the river and evolve an estimate of the current state of the system forward in time.  The estimate of the current state of the system may be obtained by a sophisticated mathematical blending of information from previous forecasts with recent observations via data assimilation.

Remote sensing and data assimilation

In data assimilation we compare model forecast predictions and observations and adjust the model state so that it is closer to the observations, bearing in mind the uncertainty in the observations. However, the quantities predicted by the model are not usually the same as those being observed by the operational observation network. For example, in weather forecasting the model may predict wind, temperature, pressure and humidity. A weather radar on the other hand sends out pulses of electromagnetic waves and measures the intensity of the returned signal as the waves bounce off raindrops in the atmosphere. Thus we require a mathematical model that describes the physical relationship between the predicted quantities and the observations.  In data assimilation, this mathematical model is often termed the observation operator.

Observation uncertainty

When we compare the model predictions to the observations using the observation operator we are typically left with a residual known as the observation uncertainty. In FRANC we are working on improving the treatment of observation uncertainty in data assimilation for convection permitting weather forecasts. This has the potential to make improvements in weather forecast accuracy and give better value for money for the observations.