

h1. Bayesian uncertainty analysis



h1. N2O emission from nitrification






{{>toc}}



# Math markup






h2. Description



Here is some math markup: $`a^2 + b^2 = c^2`$






$x^{yield}_{t}$



Or more complicated:



$`\sum_{i=1}^n i^3 = \left( \frac{n(n+1)}{2} \right)^2`$






Parameter determination for processes in LPJmL is mostly achieved by



literature values. In case, data are available, the estimation of



uncertainties and evaluation of current parameterization is possible by



Bayesian analysis. Here, we give an example how to use data for a better



grass parametrization.



It's based on $`\KaTeX`$






h2. Details



# GitLabspecific markup



I can refer to a specific commit, just by pasting the hash here: b3ede2e52b64026c68d90519d93b3bce58f4c46d






a more detailed description of it (data sources, data preparation,



meaning, usage...). Refer to references if you have any using



footnotes\[1\]



Or here: 80fbf7b1627d45d8d857481585d23430fb9b354b






h2. Technical Note



I can refer to an issue, starting with the $`#`$: #2






What you need are \* data \* the R package FME\[1\]



Here is another wiki page about [Something Else](somethingelse)






Following the procedure there, you can \* define a cost function that



gives the deviation of the model output from the observations \*



determine the local sensitivity to a large set of parameters \* evaluate



the most prominent parameters that should be included in the Monte Carlo



simulations by determining the collinearity \* fit the model to the data



using the chosen subset of parameters \* perform the Markov chain



MonteCarlo simulations \* evaluate the uncertainty of the model output



due to the parameter values accepted in the Monte Carlo chain.



# Another heading



 [ ] a task



 [x] a completed task






h2. Developer(s)



========================================






Susanne Rolinski, Anja Rammig, Werner von Bloh



# h1






h2. See Also



# N2O emission from nitrification






\[\[Upscaling\]\], \[\[Downscaling\]\], \[\[Wiki\]\], \[\[Mathematical



Description\]\], \[\[Missing wiki page\]\]



"Parton et al. 1996":http://onlinelibrary.wiley.com/doi/10.1029/96GB01455/abstract gives function






Links to other Wiki pages, that are related. It doesn't matter if the



wiki page already exists or not. Also link pages that do not exist yet!



Links to existing pages are written blue, links to nonexisting pages



are writtn in red.



$`N_{N2O} = N_{H2O} \cdot N_{pH} \cdot N_T \cdot (Kmx + Nmx \cdot N_{NH4})`$






h2. References



with



$N_{N2O} = ((WFPSb)/(ab))^{d\cdot (ba)/(ac)} \cdot ((WFPSc)/(ac))^d$



* $WFPS$ is water filled pore space of the soil



* parameters $a$ to $d$ given for sandy and medium soil



* source for functions given as Doran et al. 1988






fn1. K. Soetaert and T. Petzoldt (2010): Inverse Modelling, Sensitivity



and Monte Carlo Analysis in R Using Package FME. Journal of Statistical



Software, 33, 3, 128. 


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$N_{pH} = 0.56+1/\pi\cdot \arctan(\pi\cdot 0.45 \cdot(pH5))$



* we ignore this limitation






$N_T = 0.06+0.13\cdot \exp(0.07 \cdot T_{soil})$



* based on data by Sabey et al. (1959)






$Kmx = 0.00038$ gN m$^{2}$ d$^{1}$



* N turnover coefficient



* site specific but given for different sites



* for natural soils given as 3.8 and 3.9 (gN ha$^{1}$ d$^{1}$)






$Nmx = 0.003$ gN m$^{2}$ d$^{1}$



* maximum nitrification flux of N$_2$O with excess NH$_4$.






$N_{NH4} = 1  \exp(0.0105\cdot NH4)$



* NH4 here given as $\mu$g N per g soil



* in the same range as gN m$^{2}$ so that formula taken as it is






Process is incorporated in source:branches/nitrogen_rev2142/src/soil/littersom.c after mineralization. 


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