Modify the MinimumNConc from constant into stage based values for Wheat Grain

[byzheng]

Working on #3605.

This pull request is to test alternative method proposed in #10128 for wheat.

The parameter MinimumNConc of wheat grain is modified from constant 0.0123 to a stage based values.

• before flowering as constant 0.0123
• after flowering as stage based values

FYI: @EnliWang, @hut104, @HamishBrownPFR

[EnliWang]

Thanks Bangyou to get this moving. Is the value of 0.0123 based on literature or some measured data?

Would be interested to see how it impacts on the results.

[byzheng]

0.0123 Is the original value of MinimumNConc

[byzheng]

Proposal: Convert the minimum nitrogen concentration from whole grain into dynamic curve

Concept

This proposal introduces a new method to determine the minimum nitrogen concentration (Nₘᵢₙ) for wheat grain during the grain filling period (i.e. parameter MinimumNConc in APSIM NG for wheat grain).

1. The daily minimum nitrogen concentration ( $N_{\min}(t)$ ) reflects the requirement to fill different components into grain (e.g. protein, starch) from Anthesis to Maturity.
2. The overall average minimum nitrogen concentration in the entire grain (from anthesis to maturity) is

$$ \bar{N}_{\min} = 0.0123 $$

It reflects the measurable minimum nitrogen concentration in the whole grain through field experiments.

3. The thermal time (°Cd) for key grain development phases are:
   • From Anthesis (GS 8) to Maximum Grain Length (GS 9): ($T_1 = 120 °Cd$)
   • From Maximum Grain Length (GS 9) to End of Grain Filling (GS10): ($T_2 = 545 °Cd$)
4. The grain mass at the end of Maximum Grain Length is 10% of the potential grain mass.
5. The minimum nitrogen concentration in the grain remains constant from Anthesis to Maximum Grain Length,
   and then gradually decreases to near zero (as required by APSIM NG) at mid-grain filling (GS 9.5).

This curve is not the actual curve using in the pull request. Just a demonstrate of the curve shape.

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Derivation

Let $N_{\min}(0)$ represent the minimum nitrogen concentration required at Anthesis (stage 8).

During early grain filling (T₁), the grain contains approximately 10% of its final mass.
During late grain filling (T₂), the remaining 90% of mass accumulates while minimum nitrogen concentration declines linearly to zero by mid-grain filling.

Thus, the overall average minimum nitrogen concentration across the grain filling period can be expressed as:

$$ \frac{N_{\min}(0) \times T_1 \times 0.1 + N_{\min}(0) \times T_2 \times 0.9 / 4}{T_1 \times 0.1 + T_2 \times 0.9} = \bar{N}_{\min} $$

Solving for $N_{\min}(0)$:

$$ N_{\min}(0) = \frac{\bar{N}_{\min} \times (T_1 \times 0.1 + T_2 \times 0.9)}{T_1 \times 0.1 + T_2 \times 0.9 / 4} $$

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Example Calculation

Using:

• $\bar{N}_{\min} = 0.0123$
• $T_1 = 120$
• $T_2 = 545$

$$ N_{\min}(0) = \frac{0.0123 \times (120 \times 0.1 + 545 \times 0.9)}{120 \times 0.1 + 545 \times 0.9 / 4} \approx 0.0459 $$

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Interpretation

• The estimated minimum nitrogen concentration of grain at Anthesis is ~0.0459.
• This value represents the initial nitrogen concentration needed to maintain a final grain average of 0.0123 under the assumption of constant grain filling duration and decreasing nitrogen requirement during later stages.
• This approach provides a more biologically consistent representation of nitrogen dynamics during grain filling compared to using a fixed minimum value throughout development.

[byzheng]

Hi @EnliWang @hut104 and @HamishBrownPFR, I proposed a new idea to convert the minimum nitrogen concentration from whole grain to dynamic curve. See my comments above.

The new value is 0.0459.

It seems this new values generated better results than the arbitrary values I used before.

The performance test

• Maintained crop yield performance,
• Improved nitrogen concentration realism, and
• Preserved system stability across diverse datasets.

A summary table from ChatGPT

Aspect	Effect of Update
Wheat yield & biomass	Stable to slightly improved
Grain nitrogen & protein	Noticeably improved
Soil & nutrient balance	Unchanged
GxExM & secondary systems	Neutral to minor variation
Overall stability	Maintained — no degradation observed

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