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cyclo inversion results
A “control” or “base” case inversion has been performed with the Level II TransCom model output submissions to estimate the monthly fluxes in a stationary seasonal cycle. We employ a Bayesian synthesis inversion formalism, specifying prior estimates of both the fluxes and their uncertainty, and optimizing with respect to atmospheric observations which are also uncertain.
The basic elements for this inversion are as follows:
We invert 5-year (1992-1996) mean measurements for each month at 75 sites taken from the GLOBALVIEW-2000 dataset. This station set is identical to that used in the annual mean inversion except in the cyclostationary inversion, the station in Darwin, Australia was removed due to recent work showing Darwin as unrepresentative of the region.
The uncertainty attached to each data value, C(D), was derived from the monthly residual standard deviation (RSD) of individual observations around a smoothed time series as given by GLOBALVIEW. This choice was based on the assumption that the distribution of RSD (higher RSD values for northern and continental sites and lower RSD values for southern hemisphere oceanic sites) reflects the high-frequency variations in transport and regional flux that large-scale transport models are unable to accurately simulate. GLOBALVIEW-CO2 [2000] provides monthly rsd values averaged over 1979-1996 and annual rsd values for each separate year. To obtain monthly values for 1992-1996 we scale the 1979-1996 monthly values by the ratio of the 1992-1996 mean annual rsd to the 1979-1996 mean annual rsd.
Direct use of the RSD values for the data uncertainty results in a total reduced x2 that is much smaller than unity. This indicates that the predicted concentrations fit the data much better than the uncertainty assigned to the data itself and that the uncertainty should be reduced. The aim is to scale the RSD such that the inversion produces a total C2 of 1.0. When making this adjustment we limit the reduction such that the minimum uncertainty at any site is equivalent to 0.25 ppm on the annual mean concentration and we also adjust the uncertainty for data records that are co-located. The details are as follows: the RSD was divided by (3.6*P)0.5 where P is the proportion of real data in the record and 3.6 is chosen to satisfy our total C2 criteria. These monthly uncertainties were converted to equivalent annual uncertainties with the following expression:
where sa is the equivalent annual uncertainty, sm is the monthly uncertainty, and A represents the autocorrelation timescale for the specific station (typically around 4 months). If the annualized uncertainty was less than the minimum uncertainty used in the annual mean control inversion of 0.25 ppm, the monthly uncertainty values were increased to an uncertainty given by:
Finally, the uncertainty was increased for those sites that are likely to occur in the same model grid-cell. These adjustments gave values ranging from 0.17 ppm for a given month at remote, “clean air” sites to 4.8 ppm for continental, “noisy” sites and a mean total x2 averaged across the models of 1.0.
Two datafiles are used in the process of calculating the inverse fluxes. One is a station list file and the other is the concentration data and the associated uncertainty.
Here is the link to the netCDF 75 station datafile.
Here is the link to the station list.
Prior estimates of the fluxes in each of the 264 region/month flux combinations were determined from independent estimates of terrestrial and oceanic exchange. The land region prior flux estimates incorporate results from recent inventory studies and are identical to values used in the annual mean inversion. Where more than one estimate for a given region was considered, a mid-point of the estimate spread was used. Because the land region prior fluxes are only available as annual mean values, these were distributed evenly over those months considered the most likely to capture the emission or uptake implied by the prior flux. The ocean region prior flux estimates were prescribed as zero for each month.
The prior flux uncertainty is important for keeping the estimated fluxes within biogeochemically realistic bounds. For land regions in a given month we chose the combination of the uncertainties employed in the annual mean control case, and 30% each of NPP and respiration provided by the CASA model of net ecosystem production.
The inversion code used for the Level II inversion was developed by Peter Rayner with further work by Rachel Law and Kevin Gurney. It is written in IDL. In addition to the observational data (above) and the prior flux/uncertainties (above), this code requires a control file which contains paths to the model response functions, direction on which pre-subtracted field to include, and information on regional aggregation.
Running the cyclostationary control inversion:
1) Download the tarred and compressed file, L2inv.tar.gz. Reconstitute ‘L2inv.tar.gz’ it in its own subdirectory ‘code/’. The files you obtain allow you to run both the cyclostationary version and the time-dependent version of the code.
2) Recompile the code. First, examine the ‘Makefile.cyclo’ file and make changes appropriate to your operating system/compiler. Also, examine the ‘pathchange.txt’ file for instructions on changing the netCDF library paths within some of the subroutines to match your system.
3) Prepare to run the inversion. There are two scripts that run the inversion. These locate the appropriate input files and write the output to specified locations. These two are ‘control.master’ and ‘doall’. The first, ‘control.master’ locates the input files which should be in the ‘files4run/’ subdirectory (created when ‘L2inv.tar.gz’ was decompressed). The master script, ‘doall’ calls ‘control.master’ and it contains a number of paths that require inspection. The first is the path to where the response functions are located. Change this to your liking. The second is the series of output files. Change those paths to your liking.
4) Run ‘doall’. A series of output files should be placed in the output subdirectory you specified in ‘doall’
5) Compare your results to the files in the ‘control.results/’ subdirectory that was created during decompression of ‘L2inv.tar.gz’
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