7.3 Experiment Design
7.3.3 Observation Error Profiles
In equation 2.8, R represents the observation error covariance matrix. It is a square matrix of dimension p × p, where p is the number of observations. It is assumed that the observation errors are uncorrelated so that only non-zero elements of the matrix are the observation variances, σ2p (Kalnay 2003, Ch 5).
For most of the data assimilation trials in this study the initial assumption is that the observation errors for AMDAR and Mode-S EHS are the same and they are un- correlated. We make these assumptions because we aim firstly to obtain a practicable configuration of the data assimilation system, using the existing Met Office operational framework for the UKV NWP model. Secondly, that aircraft-based observations are reported by aircraft that are independent of each other.
Assumed Observation Error Standard Deviation
Figure 7-1a shows the assumed vertical profile of observation error standard devi- ations, σAOBS, for temperature as used in three NWP models: HIRLAM, COSMO-
KENDA and UKV(table 2.6, page 30) lists some of their properties. Similarly figure 7-1b shows the corresponding vertical profile of σAOBS for horizontal wind. For the
UKV the observation error for AMDAR used operationally had been determined from comparisons between the Met Office Unified Model and Radiosondes (Bell et al. 1999). For COSMO-KENDA the observation error for AMDAR was derived (Schraff et al. 2016, Lange & Janjic 2016, p1457, Table 1) using the Desroziers et al. (2005) diag-
Mode-S EHS temperature (fig 7-1a green squares) is 1.5 × AMDAR. The HIRLAM AMDAR observation errors are cited by de Haan & Stoffelen (2012, p.920 Table 1) and Lindskog et al. (2001, p.452 Table 1). Both of these are identical to the profile derived byCourtier et al. (1998, p.1803 Table B1). Clearly, as the σAOBS profiles for
each model differ so this will affect the interpretation of the results and the assessment of the benefits of assimilating Mode-S EHS observations. Strajnar et al. (2015) uses an AMDAR σAOBS profile for Mode-S MRAR since these observations are assumed to
be of the same quality as AMDAR (Strajnar 2012). Similarly, Strajnar (2012) uses the same observation errors as stated by Courtier et al. (1998, p.1803 Table B1).
We also show in figure 7-1a a second larger σAOBS profile (T2) for Mode-S EHS tem-
perature for the UKV. This error profile wasthead-hoc profile estimated from routine monitoring of the observation-minus-background statistics (Hall 1992, Hollingsworth et al. 1986) using the operational version of the UKV, which does not assimilate Mode- S EHS observations.
Observation-minus-Background Statistics
Figure 7-2 shows the Met Office’s routine monitoring of the observation-minus-
background error for Mode-S EHS temperature for the period 2nd to 8th January 2015.
The left panel shows the mean bias and mean standard deviation and the right panel shows the total number of Mode-S EHS reports. The operational UKV NWP model provides the background fields and, at the time of our research, did not assimilate Mode- S EHS observations. We note that the bias is negative between the altitudes 4000 m and 6000 m, and positive above. The positive bias steadily increases from 0.0 K to 1.0 K between 4000 m and 2000 m, and is approximately 1.5 K below 2000 m. The bias below 4000 m may have contributions from background errors since the operational UKV does not assimilate Mode-S EHS, and from Mode-S EHS errors, since we have
shown in chapter6that Mach Temperature becomes increasingly variable below 1000 m.
We suggest that observation bias is more likely to be result of Mode-S EHS processing than due to the ambient temperature. This is because during this period weather conditions were calm in the south east for England, as evident from the prevailing foggy conditions.
We note that the root mean square error increases from 1.5 K at 9000 m to 2.0 K at 5000 m, 2.5 K at 2000 m, with a sharp increase to 3.5 K at the surface. This vertical
profile appears to be similar to the quantisation error studied in chapter 4 (page 55).
We note the similarity between figure7-2and profiles (a) and (b) in figure4-2(page69)
0
1
2
3
4
5
Observation Standard Deviation
0
200
400
600
800
1000
Pressure Altitude (hPa)
(a) Temperature (K). UKV AMDAR (T1) (black circles), UKV AIREP (black triangles), UKV Mode-S EHS (T2) (black squares).
0
1
2
3
4
5
Observation Standard Deviation
0
200
400
600
800
1000
Pressure Altitude (hPa)
(b) Horizontal Wind Speed Component (ms−1). For NWP models, the Mode-S EHS observation
standard deviation is the same as that used for AMDAR.
Figure 7-1: Assumed observation error standard deviation, σAOBS, profiles for (a)
temperature and (b) horizontal wind components for data types AMDAR (circles), AIREP (triangles) and Mode-S EHS (squares), as used in NWP models UKV (black), HIRLAM (green) (de Haan & Stoffelen 2012, p.920 Table 1) and COSMO-KENDA (red) (Schraff et al. 2016, p1457, Table 1) and ALADIN (yellow) (Strajnar et al. 2015)
0.50.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 [o-b] (K) 0 2000 4000 6000 8000 10000 Pressure Altitude (m)
[o-b] (K)
mean RMS 0 5000 10000 15000 20000 25000 countcount per altitude bin
Mean/RMS temperature errors (K)
Figure 7-2: The mean observation-minus-background [o-b] for Mode-S EHS temper- ature for the period 2nd to 8th January 2015. The left panel shows the mean bias
(green) and root mean square error (blue). The right panel shows the total number of reports for altitude bin widths 150 m. The operational version of the UKV provides the background.
standard deviation of quantisation error, and the increase in error between 2000 m and
0 m appears to be closer to profile (a) for the full precision error. We note thatBallard
et al.(2017) show the observation-minus-background mean bias profile for March 2016 is approximately 0.5 K for all altitudes but the RMSE profile is similar to that shown
in figure7-2.
The Met Office’s routine observation monitoring shows that the Mode-S EHS tem- perature error is greater than the assumed AMDAR observation error, and the error increases significantly below 1000 m . The monitoring suggests that for Mode-S EHS
temperature in the altitude range 15,000 m (100 hPa) to 3000 m (700 hPa) σAOBS lies
somewhere between AMDAR and AIREP, between 3000 m and 100 m (1000 hPa) the
σAOBS is approximately the same as AIREP, and near the surface the σAOBS is at its
greatest. From this monitoring we construct an ad-hoc σAOBS profile, T2, which we
can use for Mode-S EHS σAOBS temperature.
The profile of this observation-minus-background error is similar to those shown in
figures 4-9 (page 83) and 6-14b (page 149), which suggests that quantisation error is
a significant contributor to the observation error for Mode-S EHS Mach Temperature.
operational UKV NWP model. We assume that it is in reasonable balance with the
other observation types (Ballard et al. 2017) since we know that the operational data
assimilation accepts aircraft observations using the σAOBS for AMDAR and AIREP.