Improved LOBSTER documentation for Alkalinity and Remineralization?

[kgrabb]

Hi all and @jagoosw,

I am trying to build my own box model based on the LOBSTER equations to first amend some processes in a simplified environment before integrating it into OceanBioME. Therefore, I have been following the LOBSTER documentation here and comparing my box model with the Box Model example code (Box.jl). As I compare the two models, I see major differences that I am needing to amend for the alkalinity equation, and what I assume is, remineralization processes.

In LOBSTER (carbonate_system.jl), it looks like the main alkalinity equations are only accounting for nutrient uptake via nitrate (+1 Alk) and calcite uptake (-2 Alk). However, to get my model to match the Box.jl model, I have to add in processes such as remineralization, nitrification, and ammonium uptake. Are there other ways Alkalinity is altered after the source code and is there documentation to show what other processes are being considered?

Similarly, my model agrees pretty well for the first 75 days. However, after 75 days, it looks like Box.jl shows remineralization with an increasing NH4 peak. I cannot simulate this using just the LOBSTER equations. Are there remineralization processes included in the DOM, sPOM, and/or bPOM that are not included in the current documentation?

Thank you for any updated documentation you can share with the complete equations written out! I appreciate the quick correspondence and informative discussions!

Cheers,
Kalina

[jagoosw]

Hi Kalina,

Thank you for reaching out! This sounds a bit strange.

I just noticed that the documentation is missing a P in the $NO_3$ and $NH_4$ equations (fixing in #335 ) and they should read:
$\frac{\partial NO_3}{\partial t} = -\mu_PL_{PAR}L_{NO_3}P + \mu_nNH_4,$
and
$\frac{\partial NH_4}{\partial t} = -\mu_PL_{PAR}L_{NH_4}P - \mu_nNH_4 + \alpha_P\gamma\mu_P L_{PAR}\left(L_{NO_3} + L_{NH_4}\right)P + \alpha_Z\mu_ZZ + \alpha_{d}\mu_{sPOM}sPOM + \alpha_{d}\mu_{bPOM}bPOM + \mu_{DOM}DOM.$

Its a bit strange that you have to add the other processes to get it to match because the code is the same as the docs:

OceanBioME.jl/src/Models/AdvectedPopulations/LOBSTER/carbonate_system.jl

Lines 41 to 44 in 8c4a080

	@inline (lobster::LOBSTER{<:Any, <:Any, <:Any, <:CarbonateSystem})(i, j, k, grid, ::Val{:Alk}, clock, fields, auxiliary_fields) = (
	nutrient_uptake(lobster, i, j, k, Val(:NO₃), fields, auxiliary_fields)
	- calcite_uptake(lobster, i, j, k, fields, auxiliary_fields)
	)

OceanBioME.jl/src/Models/AdvectedPopulations/LOBSTER/biology.jl

Lines 154 to 170 in 8c4a080

	@inline function nutrient_uptake(lobster::PHYTO_ZOO_LOBSTER, i, j, k, val_name::Val{:NO₃}, fields, auxiliary_fields)
	μ = phytoplankton_growth(lobster, i, j, k, fields, auxiliary_fields)
	kNO₃ = lobster.biology.nitrate_half_saturation
	kNH₄ = lobster.biology.ammonia_half_saturation
	ψ = lobster.biology.nitrate_ammonia_inhibition
	@inbounds begin
	NO₃ = fields.NO₃[i, j, k]
	NH₄ = fields.NH₄[i, j, k]
	end
	nitrate_limitation = NO₃ * exp(-ψ * NH₄) / (NO₃ + kNO₃)
	ammonia_limitation = max(0, NH₄ / (kNH₄ + NH₄))
	return μ * nitrate_limitation / (nitrate_limitation + ammonia_limitation + eps(0.0))
	end

OceanBioME.jl/src/Models/AdvectedPopulations/LOBSTER/biology.jl

Lines 346 to 353 in 8c4a080

	@inline function calcite_uptake(lobster::PHYTO_ZOO_LOBSTER, i, j, k, fields, auxiliary_fields)
	R = lobster.biology.redfield_ratio
	ρ = lobster.biology.carbon_calcate_ratio
	μP = phytoplankton_growth(lobster, i, j, k, fields, auxiliary_fields)
	return 2 * ρ * μP * R
	end

(Thinking about it now I'm not sure if the alkalinity should include an ammonia uptake term. This formulation was from this paper but maybe it needs an additional term?)

As for the DOM/sPOM/bPOM, I think the docs are correct, e.g. sPOM:
$\frac{\partial sPOM}{\partial t} = f_s[\left(1-a_Z)\left(G_P + G_{sPOM}\right) + m_PP^2 + m_ZZ^2\right] - G_{sPOM} - \mu_{sPOM}sPOM - \frac{\partial}{\partial z}(sPOM w_{s})$

OceanBioME.jl/src/Models/AdvectedPopulations/LOBSTER/detritus.jl

Lines 149 to 153 in 8c4a080

	@inline (lobster::TWO_PARTICLE_SIZE_LOBSTER)(i, j, k, grid, val_name::Union{Val{:sPOM}, Val{:sPON}}, clock, fields, auxiliary_fields) = (
	lobster.detritus.small_solid_waste_fraction * solid_waste(lobster, i, j, k, fields, auxiliary_fields)
	- grazing(lobster, i, j, k, val_name, fields, auxiliary_fields)
	- lobster.detritus.small_reminerlisation_rate * small_particulate_concentration(lobster.detritus, i, j, k, fields, auxiliary_fields)
	)

OceanBioME.jl/src/Models/AdvectedPopulations/LOBSTER/biology.jl

Lines 243 to 256 in 8c4a080

	@inline function solid_waste(lobster::PHYTO_ZOO_LOBSTER, i, j, k, fields, auxiliary_fields)
	α = lobster.biology.zooplankton_assimilation_fraction
	mᴾ = lobster.biology.phytoplankton_mortality_rate
	mᶻ = lobster.biology.zooplankton_mortality_rate
	@inbounds begin
	P = fields.P[i, j, k]
	Z = fields.Z[i, j, k]
	end
	G = total_grazing(lobster, i, j, k, fields, auxiliary_fields)
	return (1 - α) * G + mᴾ * P^2 + mᶻ * Z^2
	end

But there might be a discrepancy somewhere. Do you have the sinking term in your box model? I think we have no advection in our box model so if you are sinking particles out and box.jl isn't then maybe thats causing the increased $NH_4$ after remineralisation.

Sorry I couldn't be more helpful, let me know if you have more questions! If you don't mind sharing your code maybe that would help me spot the differences.

Jago