Experiments with Empirical Errors in Synthetic Observations to Improve Realism of the NCEP OSSE Assimilation System

J. S. Woollen

Abstract

1) Observations are synthesized for OSSE experiments by combining a "true" value (i.e., from a "nature" run background) with some type of noise, aka observation error.

2) Adding strictly random noise to synthetic observations does not appear to adequately model observation errors found in real data. Such experiments generally produce forecast results which are unrealistically good, especially in the Southern Hemisphere.

3) A method is desired for deriving more realistic synthetic observation error fields, which would model systematic errors of representativeness as well as the random components of observational errors. This report examines the use of an empirical estimate of observation error, namely observation-analysis from a real assimilation, applied to synthetic observations at every corresponding point in space and time over the experiment period.

4) Results of the experiments suggest that (o-a) is a suitable estimate of real observation error fields. Some adjustment of the magnitude of the o-a fields were required in the SH, possibly to account for large scale unrepresentativeness of observations in data sparse regions.

True Value - the perfectly true ob value at this point, wrt the model grid

Instrument error - errors from measuring/transmitting (not analyzed)

Representative error - unrepresentative components (not analyzed)

Analyzed error - observation content erroneously analyzed

1) Analyzed error has representative and instrument errors

2) Combination of unanalyzed errors ~ (o-a)*

* (observation-analysis) also contains forecast and other errors, and does not include analyzed ob error, but with an efficient assimilation, these should in general be small relative to the unanalyzed ob errors.

Reasons (o-a) is analogous to observation error

Given: <(o-a)**2> = EoEo + EaEa - 2EoEa

If the assimilation system is efficient,

then, EaEa 2EoEa ,

and, <(o-a)**2> is a lower limit of EoEo .

Systematic error components in (o-a)

Significant biases in the o-a field do appear in the regions we would expect to find systematic representative errors, that is, in the jet region and near the surface. The implication is, these errors are similar to what we want to include in the synthetic data.

Meteorological significance of real (o-a) may not be just right in the nature run atmosphere. Future experiments include iteration of (o-a) fields from synthetic data experiments to see if the error fields adjust to the nature run synoptic regimes.

Components of OSSE Observation Files

Source Contents Component

Fitting Real Topography in Synthetic Observations

- synthetic observations need real elevations

- use reported height plus instrument height

- extrapolation from NR introduces rep error

Extrapolations made to surface data

When the real elevation is lower than the NR:

a) NR surface pressure reduced hydrostatically to the real observation height. This becomes the "perfect" Ps.

b) NR temperature is lapsed in pressure to the perfect Ps obtained above.

c) NR moisture and winds are linearly extrapolated to the perfect Ps. The perfect Ps for winds is adjusted to reflect platform height.

d) Elevation reported in real data is retained in the synthetic observations.

Forecast results from 4 synthetic observation schemes

compared to real cases

perfect data with real surface elevations

data with random error and NR surface elevations

data with (o-a) added to surface and ½(o-a) added above

data with (o-a) added to surface and 2(o-a) added above

real data assimilation results

Conclusions

1) Using real (o-a) to supply random and systematic errors empirically to synthetic observations for OSSE experiments seems to be a viable concept.

2) Forecast results suggest that application of 1*(o-a) is suitable in the NH, and 2*(o-a) gives good results in the SH. A composite application of the errors then would be in order. For example, 1*(o-a) from 90N to 20N, a linear adjustment towards 2*(o-a) from 20N to 20S, and 2*(o-a) from 20S to 90S.

3) It may be possible to improve the synoptic correspondence of the synthetic errors by iterating (o-a) from calibration experiments.