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Model Data Assimilation, overview
Data assimilation is an analysis technique in which the observed information is accumulated into the model state.
Approaches to Data Assimilation
There are three basic approaches to data assimilation:
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The four basic types of assimilation are depicted schematically in Fig2A.6-1. Compromises between these approaches are possible. The aim is to assimilate data in a manner which does not produce sudden jumps in analysed values and some sort of continuous assimilation seems preferable. It is expensive in computing time and a compromise has been adopted with 4D-Var assimilating data observed at various times over several hours. This avoids sudden jumps at in analyses for the forecasts (e.g. 00UTC, 12UTC). Continuous Assimilation is used during 4D-Var analysis process for the early cut-off analysis.
Fig2A.6-1: Representation of four basic strategies for data assimilation as a function of time. Observations are made at different times and arrive at irregular times. Intermittent assimilation of observations induces step changes in the model analysis (red line) while continuous assimilation of observations gives smoother changes in the model analyses.
Quality Control
Data is quality controlled using constraints of:
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- Data Extraction
- Thinning (to reduce over-emphasis towards values in a small area)
- Check out duplicate reports (to remove over-emphasis of the observation)
- Ship tracks check (to ensure observations made at a reasonable location)
- Hydrostatic check
- Some data is not used to avoid over-sampling and correlated errors.
- Departures and flags are still calculated for further assessment.
- Blocklisting
- Data skipped due to systematic bad performance or due to different considerations (e.g. data being assessed as unreliable, inconsistent or misleading).
- Model/4D-Var dependent quality control
- First guess based rejections
- 4D-Var quality control rejections
- The Analysis
Outline of the analysis process
The analysis process seeks to realistically represent in the model the actual state of the atmosphere. However, inconsistencies in time and space of the observations mean that this aim will never be actually attained. The best that can be done is to approximate (hopefully closely) the actual state of the atmosphere while maintaining the numerical stability of the model atmosphere both horizontally and vertically. The assimilation process is carried out by 4D-Var (see below). In simple terms the previous analysis step has used model processes (e.g. dynamics, radiation, etc) to reach a forecast first guess value at a given location. This will usually differ from an observation at that location and time. The difference between them is the "departure". The analysis scheme now adjusts the value at the location towards the observed value while retaining stability in the model atmosphere. This adjustment is the "Analysis Increment". If the magnitude is large it suggests the model is not capturing the state of the atmosphere well (e.g. a jet is displaced, a trough is sharper, large scale active convection has not been completely captured). However, a large Analysis Increment may also suggest poor data. Analysis Increment charts are a powerful tool for identifying areas of uncertainty which might propagate downstream.
Fig2A.6-2: Schematic of the data assimilation process (from a diagnostic perspective). All the model forecast parameters (dynamics, radiation, etc.) are used in the model forecast to deliver the first guess forecast (red). The observations (grey) however will normally differ to a greater or lesser extent from the first guess forecast (red). The analysis increment (yellow) is evaluated to bring the the evolution more into line with the observations while maintaining model stability. The resultant value (blue) becomes the first guess for the next analysis.
Model Data Assimilation, 4D-Var
The four-dimensional variational analysis (4D-Var) system uses an optimisation procedure to adjust the initial condition to obtain:
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To estimate the flow-dependent uncertainty, a set of 3-hour forecasts, valid at the start of the 4D-Var time-window, is computed from 25 perturbed, equally likely analyses. Small variations are imposed on the observations and the sea surface temperature to reflect uncertainties, and also within the error parameterisation to cope with uncertainties in the forecast evolution. The perturbations produced using this Ensemble of Data Assimilations(EDA) are also used for the construction of the perturbations in the forecast ensemble.
Fig2A.6-3: The ECMWF 4-dimensional data assimilation system determines a correction to the background initial condition (blue line) that leads to an analysis that is somewhere "midway" between background and observations. In simplest terms the analysis is a weighted mean of the background and observations.
Fig2A.6-4: Each observation has an error (instrumental, representativeness, etc) and error within the IFS forecast models is also taken into account. A way to simulate both these effects is to run an Ensemble of Data Assimilation (EDA). These are shown in green.
Analogies to 4D-Var and the EDA
Suppose a forecaster wants to create a sequence of manually analysed hourly synoptic charts for their region, which evolve smoothly, continuously and realistically from one time to the next, throughout. To achieve this one approach would be to draw up one chart, using all available data, surface observations, imagery etc, then another for a subsequent time in the same way. Then the forecaster might go back to the first chart, rub something out and re-draw it in a rather different fashion that still fits the available observations reasonably well, but that allows the next chart to follow on better. Then they might draw up other charts for other times, and repeat this process many times, rubbing out and re-drawing, probably all of the charts in some way or other, to achieve the final goal of sensible continuity. Each time a chart is readjusted the changes needed will become smaller and smaller, until finally the forecaster is happy that they have a full and consistent sequence. This is the forecaster's equivalent of 4D-Var. Of course in 4D-Var there is the additional constraint of full vertical consistency also, though in the forecaster world soundings and imagery may indeed be contributing in an analogous way.
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Scale-selective re-centring has been introduced in the EDA in Cy50r1. This is to improve the realism of initial conditions in the ENS, particularly for tropical cyclones. Re-centring is now only applied to large-scale upper-air fields, centring them on the control forecast, while small-scale structures come directly from the EDA. This helps avoid unrealistic 'double-centred' tropical cyclones from appearing at the start of the ENS forecasts (see Fig2A.6-5).
Additional Sources of Information
(Note: In older material there may be references to issues that have subsequently been addressed)
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