This page is just GK's musings on things at least slightly associated with the nitrogen fertilizer problem at MISG:
https://mathsinindustry.com/optimizing-fertilizer-strategy-under-uncertainty/
The people in charge of this problem were:
Alaric Korb (Royal Agricultural Society of Western Australia)
alaric.korb AT aswa.org.au
and, Moderator,
Melanie Roberts (Griffith University)
m.roberts2 AT griffith.edu.au
Neither are in way responsible for errors or misunderstandings on GK's pages.
Sadly, the problem was scrapped from those treated at the Feb 2026 MISG.
GK's pages here are left here in case it re-emerges in a later MISG to be held in Perth.
The mathsinindustry page above listed as "Objectives for the Study Group on this N-fertilizer question :
(i) Develop a reduced-order dynamical model that approximates the transport of Nitrogen through WA specific soil types (e.g., duplex soils: sand over clay) without the heavy computational cost of full hydrological simulations (like HYDRUS).
(Ground water hydrology: Perhaps others might look at book and code:
github.com/pythongroundwaterbook/analytic_gw_book)
(ii) Solve a Stochastic Optimal Control problem: Determine the optimal “stopping time” or “trigger points” for top-up fertilization. Question: Given a probabilistic forecast of rain in the next 14 days, should the farmer apply N now, wait, or abandon application?
(iii) Quantify “Leaching Risk”: creating a probability density function for nutrient loss below the root zone based on soil hydraulic conductivity and rainfall variance."
There are lots of interesting things associated with the problem, a huge amount done on related problems, but GK really really hasn't the time (or skill) to do much.
MISG26NotForGK collects miscellaneous items.
GK works a bit at Curtin. Anyway to hang on in at Curtin a bit longer (as bosses also say I'm not fitting in with their research priorities), I feel I have to fit in with Curtin Maths' interest in optimisation matters. So I guess objective (ii) is related. As regards Curtin students, 2nd year undergrad and above, they use python packages PuLP (for optimisation) and SimPy (for simulation).
Curtin/UWA have an old Fortran package MISER for optimal control.
https://www.researchgate.net/publication/279232070_VISUAL_MISER_An_efficient_user-friendly_visual_program_for_solving_optimal_control_problems
My guess is that MISER may have been superceded by something in matlab, but GK isn't going to do it.
To solve item (ii), do we need detailed models of plant growth? Specifically how does the crop respond to fertilizer and moisture over the whole growing season. There are codes for these, e.g. AquaCrop from UN-FAO (which has a python version), APSIM (from CSIRO) and many others listed at MISG26NotForGK
Might less detailed modelling suffice? Some variant of logistic growth be good enough?
(Sometimes these are run in connection with weather generators, e.g. RMAWGEN )
This NotForGK page also has a bit about soilchemn
GK There are many optimisation approaches.
Some are very simple: more on that at the Very SImple paragraph(s) below.
pymoo - multi objective optimisation - might be relevant to maximising yield at minimum nitrogen.
(But really, single objective profit= yield*saleprice - nitrogenTotal*Nprice might be better/simpler.)
For PuLP, there are various standard problems, one of which is the "Perishable Inventory Problem", and it is from this I "imagine" an extremely simplified model in which "nitrogen in the root zone" is the perishable (removable) quantity which is also consumed, and which can be restocked regularly.
Even if not esp. useful for the real fertiliser problem, it is possible it might interest students on Curtin's 2nd year "Supply Chain Optimisation" unit that things they are learning there have broader applicability than just shops, factories and logistics ... and help them to be prepared to see structure in different problems, view things abstractly when appopriate.
So far this PuLP "Perishable Inventory Problem" is, for me, just "imagined".
Very SImple There are studies on N-effects in dry land wheat farming. Because data is mostly related to final yield, and most commonly with a single application of fertilizer, the better known results are for this, specifically with other variables (ET evapotranspiration, etc.) fixed, the yield Y is approximately quadratic in N, Y=a0 + a1*N +a2*N^2, a0 and a1 positive, a2 negative. Might one be able to do something similar with biomass B (roots? stem and leaves) and more than one application of N? bquadratic
This fits with the "split applications" mentioned by google:
Google "Optimal nitrogen fertilizer" says:
Optimal nitrogen fertilizer application involves timing it with peak plant demand (growth stages), using split applications, matching fertilizer type to conditions (slow-release or inhibitors for efficiency), avoiding wet/waterlogged soils or extreme heat to prevent losses (leaching/volatilization), and ensuring proper placement (e.g., near roots, deep placement) for maximum uptake and minimum environmental impact. *Split applications*, slow-release formulas, and inhibitors (like those in enhanced-efficiency fertilizers) significantly improve N use efficiency.
More material on optimisation is at an optimisation page.
A very preliminary draft for the simple biquadratic effort is all that is there now, Feb 2026.
If/when I have anything, using more sophisticated software it might go up at some pages under the optimisation page like
MISG26PuLP
MISGpymoo
(I have unavoidable teaching commitments at Curtin afternoon Tue 17th, but my Wed classes don't start until Wed 25th.)
People from Curtin's
https://research.curtin.edu.au/optimisation/
https://www.optimisation-centre.com.au
have skills which would be useful. Some people there may have wheat farming contacts as one of the Optimisation-Centre's case studies concerned harvest optimisation, logistics, supply chain management, on-farm grain storage, etc. Very different from fertilizer problem, of course.
Should this problem develop to the stage of real work with several people involved use of zoom and overleaf will be appropriate.