Dear Reviewer,

Thank you for your careful review and valuable comments on our manuscript. Your insightful questions have been very helpful in improving the clarity and logical flow of our model description. We have addressed each of your concerns below and will incorporate the corresponding clarifications and revisions into the manuscript.

1. The parameter t is introduced too briefly in the methodology. Is t computed from 0 until NH₃ and NH₄⁺ reach equilibrium? The influence of the evolution of t on the model output is not made clear.

Response: Thank you for this comment. In the model, t represents the iteration step number, not continuous time. The model uses a discretized iterative approach to simulate the synchronous changes in NH₃ and NH₄⁺ in the atmosphere, including transformation, deposition, and isotopic composition. Each iteration represents one time step (without a specific physical duration), and the process is repeated until the system reaches a steady state (i.e., when the mass fractions and isotopic compositions of NH₃ and NH₄⁺ no longer change significantly). In the revised “2.1 Model Development” section, we will clarify:

• t is the iteration index, starting from t = 1;
• The model output is the steady-state value of δ¹⁵N₄a₋₃s.

1. It is unclear how the [NH₃d]ᵗ and [NH₄⁺d]ᵗ terms in Eq. (6) are used to calculate d15N4a-3s.

Response: [NH₃d]ᵗ and [NH₄⁺d]ᵗ represent the mass fractions of NH₃ and NH₄⁺ deposited at iteration step t. They are used in the model for isotopic mass balance calculations (Eqs. 9–10), ensuring that deposition does not affect the δ¹⁵N of the remaining NHₓ in the atmosphere. Specifically:

• The isotopic composition of the deposited fraction is assumed to be the same as that in the atmosphere at that step (Eq. 10);
• The isotopic composition of the remaining atmospheric NHₓ is updated via Eq. (8);
• Finally, δ¹⁵N₄a₋₃s is calculated using Eq. (4).

We will add a clearer description of this computational flow in “2.1 Model Development.”

1. (10) assumes that the d15N of deposition equals that of the atmosphere. How is this assumption carried into the calculation of δ¹⁵N₄a₋₃s in Eq. (4)? Also, should NH₄ in the equation read NH₄⁺?

Response:

(1) The assumption in Eq. (10) is a common simplification that deposition does not cause isotopic fractionation (only gas–particle conversion fractionation is considered). This allows the deposition process to affect only the mass fractions of NHₓ without additionally altering its isotopic composition, thus simplifying the model. The impact of this assumption has been assessed through sensitivity analysis (showing minor sensitivity to D₃ and D₄).

(2) You are correct; “NH₄” should be “NH₄⁺” throughout. We will consistently use “NH₄⁺” in the revised text.

1. How is the δ¹⁵N-NHₓ value obtained from Eq. (8) passed to Eq. (4) to compute δ¹⁵N-NH₄⁺ or δ¹⁵N-NH₃s, which is later set to 0.

Response: Eq. (8) calculates the current atmospheric δ¹⁵N-NHₓ value ([δ¹⁵N-NHₓ]ᵗ). This value is used to:

• Update the isotopic composition of atmospheric NHₓ for the next iteration step;
• It is substituted into Eq. (4) to compute δ¹⁵N₄a₋₃s, where δ¹⁵N-NH₃s is a preset source value (set to 0‰ in this study as a reference).

We will clarify this numerical transfer process in the iterative procedure described in “2.1 Model Development.”

1. In Eq. (6) the [NH3a]t is [NH3a]t-1 times 1-G4-D3. Here, Are G4 and D3 rates or ratios?

Response: In this model, G₄ and D₃ represent unitless conversion/deposition ratios per iteration step, indicating the fraction of NH₃ converted to NH₄⁺ and the fraction of NH₃ deposited in each step, respectively. They are parameterized relative values based on actual atmospheric chemistry and deposition rates.

We will explicitly state their dimensionless nature and physical meaning in “2.1 Model Development.”

1. Line 146 states that G₄/D₃ ≈ 3 %. The subsequent sensitivity tests set G4 to 0.5–2 × D3, which spans one to two orders of magnitude above this ratio.

Response: We appreciate you pointing out this potential confusion. The statement “G₄/D₃ ≈ 3%” in the original text was a typographical error, and it will be removed in the revised manuscript. In the Supporting Information (SI), we synthesized findings from numerous previous studies to establish the parameter settings of G₄ = 0.5–2 × D₃. This range was chosen to cover a wide spectrum of scenarios—from low acidic gas conditions (e.g., marine background) to high acidic gas conditions (e.g., urban pollution)—thereby extending the analysis to more extreme pollution scenarios.