
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


It's based on $`\KaTeX`$


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.








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,


Or here: 80fbf7b1627d45d8d857481585d23430fb9b354b


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




footnotes\[1\]








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


# Another heading


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


 [ ] a task


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


 [x] a completed task


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.








h2. Developer(s)


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






Susanne Rolinski, Anja Rammig, Werner von Bloh


# h1






h2. See Also


# N2O emission from nitrification






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


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


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








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


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


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.








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


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


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


* we ignore this limitation


Software, 33, 3, 128. 



\ No newline at end of file 

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




* 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. 



\ No newline at end of file 