GPSRO Monitoring - description

(O-B)/B profile plots
These plots allow us to compare statistics of the observed GPSRO bending angle or refractivity with equivalent values calculated using fields from the Met Office's global model. The fractional difference in bending angle or refractivity, referred to as (Observation-Background)/Background or (O-B)/B, is calculated for each occultation profile at a fixed set of altitude levels (200 m intervals, the (O-B)/B values were interpolated on to these levels linearly. The altitude data are geopotential height with respect to the geoid for refractivity and impact height with respect to WGS-84 ellipsoid for bending angle.
The mean of (O-B)/B over many occultations for each altitude level is calculated. Over many thousands of occultations this mean indicates the typical differences (biases) between the observed and forward-modelled values. We also show the standard deviation of (O-B)/B, indicating the width of the distribution. The plots show the number of occultations used in each mean and standard deviation calculation i.e. number that were accepted by the Met Office quality control.
Unless otherwise specified, solid lines show mean values, dashed lines show standard deviations and dash-dot lines show the number of observations.
Monthly bending angle (O-B)/B statistics provided by ECMWF have been added to a selection of (O-B)/B plots, and some ECMWF refractivity statistics are displayed for the GRAS instruments. These plots help to distinguish between observation problems and model issues.
These plots should be useful for comparing satellites/models/processing centres and thus for making decisions on which data to assimilate into NWP models.
Some notes for individual plots: Rising/Setting - this is determined by the flags in the BUFR data.

• Land/Sea - the surface type is determined by an N512 land/sea mask. The coastlines are determined if both land and sea points exist in a 5x5 box centred on each grid point.
• Day/Night - If the local solar time of an observation is between 06h and 18h, it is labelled as a daytime observation. The tilt of the Earth's axis is not accounted for.
• PCD - this shows the statistics produced using the observations that have and have not been flagged as non-nominal by the data providers (i.e. the PCD flag in the BUFR files).
• QC - This shows the statistics before and after Met Office 1D-Var-based quality control has been applied (i.e. as is done prior to assimilation).

Zonal (O-B)/B
These plots show the mean and standard deviation of (O-B)/B and the observation count averaged over latitudinal bands around the globe. Each band is 1 degree wide in latitude to ensure sufficient data for the average. The zonal averages are calculated on each altitude level, and the result is shown as a contour plot. Zonal plots for day and night are also produced which may assist in determining the cause of data problems.

Time series plots
These plots show how global (O-B)/B statistics vary with time on altitude levels. These are calculated for each 6-hour period, and are shown on a colour scale. The plots always show the data from the previous month. These plots are useful as they allow changes in the data quality of the observations or background to be seen. Also available are ECMWF and Met Office bending angle statistics against time on the same plot for a selection of impact heights; with Met Office statistics plotted every 6 hours, ECMWF every 12 hours. They help to determine whether changes with time are related to observations or the models.

Correlation plots
To get a qualitative feel for observation error covariance, the vertical correlation matrices of (O-B)/B for refractivity bending angle and refractivity are plotted against height. Although some of the correlations of (O-B)/B come from the background we can still get a feel for the observation part of error correlation by performing comparisons between satellites/processing centres, when B should be the same (although different satellites sample different local times). Also the difference between refractivity and bending angle provide an interesting comparison, and changes in correlation lengths can indicate adjustments to smoothing parameters made by the processing centres.

1D-Var histogram
At the Met Office we pass radio occultation data through a 1D-Var procedure for QC purposes prior to assimilating the data in 4D-Var; the aim of this is to black-list poor quality occultations. We run this 1D-Var in a non-operational capacity for monitoring. In operations, some instruments have their height range restricted, but for monitoring we pass observations from all heights to the 1D-Var.
The 1D-Var hist plot shows histograms of (1), 2J/m when J is the initial cost function (m is the number of observations), (2), 2J/m at convergence and (3) , the number of iterations required to obtain convergence.

Map plots
Four types of map plot are produced for each satellite/combination:

• Initial cost function. One point is shown for each profile and its colour represents the initial cost function prior to 1D-Var.
• Final cost function. One point is shown for each profile and its colour represents the value of the 1D-Var cost function on convergence.
• Map plot showing the location of all observations received, with a colour that indicates if the observation was (1) non-nominal, (2) nominal but failed QC or (3) nominal and passed QC.
• Local Solar Time. Though not strictly a map plot, this shows the local solar time and latitude of each observation. The colours are different for rising and setting occultations.

Azimuth
This plot shows a histogram of the azimuth angle, i.e. the bearing from North of the vector from the GNSS satellite to the receiving LEO satellite.

Histograms
There are two histogram figures, each of which contain histograms of (O-B)/B for a given height. These are useful to determine if biases are caused by outliers or if the whole distribution is shifted.

Time trend
There is one figure for six different height ranges, and these show:

• Mean (O-B)/B for rising and setting occultations as a function of time throughout the previous month.
• Standard deviation.
• Number of observations

Where available, ECMWF statistics are also plotted, but note that these are provided in 1km height bins, so the statistics may show variation. In particular, the number of observations from the ECMWF bins have been scaled to provide a better match to the Met Office values. Therefore, the plotted values should only be interpreted as a proxy for the number of observation; however, the trends themselves can be useful.

Matched plots

These plots show statistics of co-located observations over the period of a month. Co-located pairs of observations are identified if they occur within 300km and 3 hours of each other. Checks are in place to ensure that observations are not compared with themselves and pairs are ignored if they have already been included in the opposite order (i.e. if O2-O1 has been included in the stats, O1-O2 will subsequently be screened out).
The plotted statistics are in fact (O1-O2)/(0.5*(O1+O2)). The denominator is, therefore, the mean of the two observations. This is intended to reduce any bias artefact that might be produced if one or other observation was consistently used in the denominator.
Pairs are rejected from the statistics if the fractional difference between them is greater than 2.0.

Spatially mapped statistics

These plots show various statistics for a range of heights that have been binned onto a lat-lon grid and overlaid on a map. These plots include:

• Number of observations
• Mean of observations and Met Office backgrounds
• Standard deviations of observations and Met Office backgrounds
• Mean (O-B)/B
• Standard deviation of (O-B)/B

VAR stats

The Met Office data assimilation system, called VAR, produces a series of statistics for each assimilation window. This includes the contribution to the observation term of the cost function from each observation type. Therefore we can plot time series of initial and final cost functions, as well as the difference between these.
An additional figure shows the time series of the observations' RMS departures from the "guess" state at the start and end of the minimisation. These are shown for a range of heights.
Both of these figures are shown for the early forecast run ("glm") and the update run ("glu") which has a much later cut-off time, and hence more observations are assimilated in this run.

Delay histograms
The plots show the distribution of delay times, i.e. the time taken since the observation was made for the data to arrive in the MetDB. The solid line is the histogram of delay times for the occultations. The dashed line is the accumulation histogram, which gives the proportion of the data received at a given time. These plots are produced for yesterday's data and for a 28-day (monthly) period of data.They are important for judging how quickly the data is (or could be) assimilated into NWP models.

Data availability
The plots shows the quantity of data provided during the past 28 days. The vertical axis denotes the date (dd/mm) and the horizontal axis the UTC time of day (hh) of the observation. A coloured box is plotted for an hour and date if at least one RO profile was available in that hour; the number of profiles received is printed within the box. The colour of the box indicates the smallest delay for data observed within that hour:

• Green - under 3 hours
• Yellow - 3-6 hours
• Red - over 6 hours

The key at the bottom of the plot shows the colours used. Blank areas mean that no profiles were available in MetDB for that hour (at the time of the analysis). The total number of profiles for each day is shown on the right margin of the plot. It should be noted that the flow of data provided to the Met Office can stop occasionally for reasons beyond our control, hence why some of the plots may be missing.

Receipt Times
There is a single plot for all satellite/processing centre combos. The title shows the satellite and processing centre IDs and first and last observation times being analyzed; nominally this will be the previous 28 days. The coloured vertical 'streaks' are made up of individual points (one per RO profile), each showing the delay (in hours, vertical axis) against the time of day (receipt time, horizontal axis) that the RO profile was ingested into the MetDB (receipt time). The key at the top of the plot shows the colours used for each satellite/processing centre combo, the number of profiles in the analysis, the period of available data and the percentage of data that would have met the operational Global model Main Run nominal cut-off times (see below), for that combo. The light shaded zones (gray, pink, green, blue) denote the operational Global model analysis nominal data windows (±3hrs of the Main Run analysis times of hh=00, 06, 12 & 18 UTC). The horizontal dashed line represents the basic operational requirement that 90% of the data be available within 3h00m of the observation time, so the more points lying below this line, the better. The vertical dotted lines labeled 'Mhh' represent cut-off times for the Main Runs; data arriving after these times will not be assimilated (but they might be included in the 12Z Update Run, which cut-off is denoted by the vertical dashed line labeled 'U12').

For data to be available for operational assimilation, its observation time must be within the model analysis window and be delivered to MetDB before the cut-off time for that window. Hence data points must lie in the yellow triangles for inclusion in the Main Runs. Late-arriving data lying in the dark pink area would meet the cut-off for the U12 analysis, which isused as the starting point for the main 6-day forecast. Data not lying in a yellow or pink zone would never be assimilated in our operational system (but could be included in an off-line (re-)analysis or case study to maximize data coverage)The date and time when the plots were generated are shown in the bottom right corner.