### 2.18.2.3. Cost of Nitrogen Fixation[¶](#cost-of-nitrogen-fixation "Permalink to this headline")

The cost of fixation is derived from [Houlton et al. (2008)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#houltonetal2008).

\\\[N\_{cost,fix} = -s\_{fix}/(1.25 e^{a\_{fix} + b\_{fix} . t\_{soil} (1 - 0.5 t\_{soil}/ c\_{fix}) })\\\]

Herein, \\(a\_{fix}\\), \\(b\_{fix}\\) and \\(c\_{fix}\\) are all parameters of the temperature response function of fixation reported by Houlton et al. (2008) (\\(exp\[a+bT\_s(1-0.5T\_s/c)\\)). t\_{soil} is the soil temperature in C. The values of these parameters are fitted to empirical data as a=-3.62 \\(\\pm\\) 0.52, b=0.27:math:pm 0.04 and c=25.15 \\(\\pm\\) 0.66. 1.25 converts from the temperature response function to a 0-1 limitation factor (as specifically employed by Houlton et al.). This function is a ‘rate’ of uptake for a given temperature. Here we assimilated the rate of fixation into the cost term by assuming that the rate is analagous to a conductance for N, and inverting the term to produce a cost/resistance analagoue. We then multiply this temperature term by the minimum cost at optimal temperature (\\(s\_{fix}\\)) to give a temperature limited cost in terms of C to N ratios.

