Field measurements were carried out on an arable plot located near Kartal, Hungary, at the Gödöllő Experimental Farm. The observation period covered the late summer to early autumn growing season, extending from 28 August to 21 October 2025. The geographic coordinates of the site are 47°39^′42.56^′′ N, 19°31^′43.21^′′ E, with an elevation of approximately 153 m above sea level.

The region is characterized by a continental climate, with a long-term (1991–2020) mean annual precipitation of 550–600 mm. During the measurement campaign, cumulative precipitation amounted to 65 mm, resulting in predominantly dry soil conditions.

The soil at the site is classified as a Haplic Phaeozem (Humic, Pantoloamic) according to the World Reference Base for Soil Resources. Particle size analysis indicated a composition of 32.3 % clay, 49.1 % silt, and 18.6 % sand, corresponding to a silty clay loam texture under the USDA classification scheme.

Field management prior to and during the experiment included mineral fertilization and crop establishment. On 25 August, the field was fertilized with 200 kg ha⁻¹ of granular diammonium phosphate, equivalent to 30 kg N ha⁻¹ and 80 kg P ha⁻¹. Winter rapeseed (Brassica napus L.) was sown 2 d later, on 27 August. As a result, the measurement period encompassed a transition from bare soil conditions immediately after fertilization to a developing crop canopy by mid-October.

The turbulent ammonia flux was calculated using the aerodynamic gradient method with a 30 min averaging time interval at two measurement heights (z1 = 0.39 m, z2 = 3.00 m). During the calculations, the displacement height (d) was assumed to be 0.05 m. The friction velocity (u*) and the Monin-Obukhov length (L) were measured and/or derived using an eddy-covariance measurement system. Flux calculations were based on Monin–Obukhov similarity theory (MOST) using a range of universal similarity functions reported in the literature; additionally, turbulent fluxes were also determined using the simplest logarithmic profile approximation.

A widely used approach for flux calculations based on trace gas gradient measurements is the application of universal stability functions that depend on atmospheric stability. Since NH₃ can generally be treated as a passive scalar in the surface layer, universal similarity functions developed for sensible heat transfer are commonly applied in aerodynamic gradient studies. This methodology has been used, among others, by Phillips et al. (2004), Spirig et al. (2010), Toyota et al. (2016), Kułek and Weidinger (2023), Zahn et al. (2023), and Abdulwahab et al. (2025), and is also described in methodological overviews of modern micrometeorological measurement techniques (Trebs et al., 2021).

In the case of stable stratification, 30 universal functions were applied together with logarithmic profiles characterized by two different Prandtl numbers (Tables A1 and A3), whereas under unstable stratification 22 universal functions were used together with two logarithmic profile formulations (Tables A2 and A3). These were selected based on the synthesis studies of Högström (1988), Weidinger et al. (2000), Prueger and Kustas (2005), Kramm and Herbert (2009), Foken (2017), and a case study by Kułek and Weidinger (2023), as well as studies addressing turbulent exchange processes of trace gases. In addition to the classical logarithmic profile assumption (Prandtl number Pr = 1), several universal functions widely used in the literature were applied, such as those proposed by Businger et al. (1971) and Dyer (1974), later reformulated by Högström (1988).

The concentration gradient (Eq. 1) was expressed based on Monin–Obukhov similarity theory, adopting the commonly used assumption that the universal function describing trace gas transport has the same functional form as that for sensible heat transport φc(ζ) ≡ φH(ζ) (Mayer et al., 2011; Zahn et al., 2023; Abdulwahab et al., 2025). The profile equation for concentration gradient is 1∂c‾∂ln⁡z-d≅Δc‾Δln⁡z-d=c‾2-c‾1ln⁡z2-d-ln⁡z1-d=c∗κφcζk where c∗ is the dynamical concentration scale for the NH₃ flux calculation, c‾1 and c‾2 are the 30 min mean concentrations.

Assuming a near-logarithmic profile, the dimensionless height was defined as ζk = zk/L, where zk denotes the geometric mean height of the two measurement levels: 2zk=z1-dz2-d

Although the integral form of Eq. (1) could also be applied (Weidinger et al., 2000; Foken, 2017; Foken and Mauder, 2024), for two closely spaced measurement levels the direct calculation using Eq. (1) provides sufficiently accurate results. Comparative calculations were performed using the two most commonly applied universal functions (Businger et al., 1971; Dyer, 1974), revealing negligible differences between the two approaches.

Universal functions have generally been validated within the interval -1 ≤ ζ ≤ + 1. In extremely stable (ζ > 1) or extremely unstable (ζ < -1) conditions – representing approximately 2 % of the cases – the critical dimensionless heights (ζkrit = 1, if ζ > 1, ζkrit = -1, if ζ < -1) was applied in the calculations, while retaining the original stability classification.

The ith type of dynamical concentration scale, c∗i was calculated based on the corresponding universal function, φci(ζk) and von Karman-constant, κi from Eq. (1): 3c∗i≅κiφciζkc‾2-c‾1ln⁡z2-d-ln⁡z1-d. The 30 min ammonia flux was obtained by averaging the individual flux estimates: 4FNH3=1N∑i=1N-u∗c∗i, where N = 30 for stable or neutral stratification (ζk ≥ 0) and N = 22 for unstable (ζk < 0) stratification, including the two logarithmic profile approaches in both cases (Appendix, Tables A1–A3).

To evaluate methodological robustness, fluxes were calculated using a comprehensive ensemble of universal similarity functions under both stable and unstable stratification. Sensitivity analysis showed that the variability attributable solely to stability-function selection remained small relative to observed diurnal flux amplitudes, indicating that the dominant uncertainty did not arise from similarity-function choice.

Because ammonia flux time series inherently exhibit strong autocorrelation and non-stationarity, strict chronological validation was implemented to prevent temporal leakage. This design ensures that predictive performance reflects genuine forward extrapolation in time rather than artefacts arising from random data partitioning.

Half-hourly NH₃ fluxes (nmol m⁻² s⁻¹) were analyzed over a multi-day post-fertilization period (n = 2590 observations). The dataset included a comprehensive set of candidate predictors encompassing structural variables (leaf area index), soil physical properties (volumetric water content, water-filled pore space, soil temperature), meteorological drivers (air temperature, relative humidity, precipitation, global radiation, photosynthetically active radiation), turbulent exchange parameters (friction velocity, momentum flux, sensible and latent heat fluxes, wind speed and direction, Monin–Obukhov length), chemical variables (NH₃ concentration at 3 m), management-related variables (days after fertilization), and derived aerodynamic and boundary layer resistances. All predictors were initially included in the model without subjective pre-selection.

The flux time series exhibited three dominant structural characteristics: a pronounced diurnal cycle with nighttime minima and daytime maxima, a progressive decay following fertilizer application, and strong short-term autocorrelation at sub-daily scale. Because these properties violate assumptions of independence and stationarity, a time-aware modelling framework was adopted.

To prevent temporal leakage, model validation was conducted using a strictly chronological split. The first 80 % of days were used for training and the remaining 20 % were reserved as an independent test set representing forward prediction in time. No random cross-validation was applied.

Model performance was evaluated exclusively on the final 20 % of days, chronologically withheld from model training to represent forward prediction in time, using the coefficient of determination (R2), root mean square error (RMSE) and mean absolute error (MAE).

To account for short-term dynamical persistence, autoregressive lag features were introduced to represent short-term temporal persistence in the NH₃ flux time series.

Specifically, NH₃ flux values from the previous six half-hour intervals (NH_3t−1 to NH_3t−6), corresponding to a 3 h memory window, were included as predictors. Lagged values crossing day boundaries were masked to avoid artificial carryover effects.

The term “memory” is used here to describe the apparent temporal persistence of the NH₃ flux time series, rather than instrumental carry-over. Since the residence time in the sampling line was only about 3.8 s and each inlet switch was followed by a 1 min flushing period, instrumental memory cannot explain the observed persistence over several half-hourly intervals. The lag dependence is therefore interpreted as a property of the soil–surface–canopy exchange system, reflecting the gradual evolution of the surface NH4+ / NH₃ reservoir, soil temperature and moisture conditions, adsorption–desorption processes, and persistent turbulence regimes.

A tree-based ensemble regression model was employed to capture nonlinear relationships and high-order interactions among meteorological, surface, turbulence-related, and autoregressive predictors without assuming linearity. Missing values were handled using median imputation fitted on the training dataset and applied consistently to the test data.

To interpret model structure and underlying mechanisms, three complementary approaches were applied: impurity-based and permutation feature importance to identify dominant predictors, Partial Dependence (PDP) and Individual Conditional Expectation (ICE) curves to visualize nonlinear responses, and Friedman's H-statistic to quantify the strength of pairwise nonlinear interactions. Residual autocorrelation within days was additionally evaluated using autocorrelation functions (ACF) to assess remaining temporal structure after modelling. Finally, regime-specific analyses were performed separately for daytime (PAR > 0) and nighttime (PAR = 0) conditions to identify potential shifts in dominant environmental controls.

To assess the measurement reliability and random uncertainty of the system, samples were collected at a single inlet height, applying two-minute temporal averaging. This averaging strategy suppresses short-term fluctuations and ensures that the comparison predominantly reflects instrumental and sampling uncertainties, rather than environmental variability.

During the comparison period, both sampling channels operated at an identical height of 300 cm. Under these conditions, the agreement between the two datasets was excellent. The Pearson correlation coefficient (r = 0.97) indicates a strong linear relationship. Linear regression yielded a = 0.97 × b + 0.60, demonstrating an almost one-to-one correspondence with only a minor offset (Fig. 1).

The small mean offset of +0.28 ppb was negligible relative to the standard deviation of the differences (2.06 ppb), suggesting that the observed deviations were dominated by instrumental noise and sampling uncertainty.

Based on these results, the typical random measurement uncertainty between the two channels under identical sampling conditions is estimated to be ±2 ppb (1σ). Accordingly, the upper bound of the random error at the 95 % confidence level (±1.96σ) is approximately ±4 ppb.

Because inlet-related adsorption/desorption may represent a potential source of bias in NH₃ measurements, an additional in situ inlet-length test was performed to evaluate its effect under the operating conditions of this study. The test showed that the dynamic inlet-induced bias was negligible compared with the measurement uncertainty; the test design and results are presented in Appendix B.

Ammonia fluxes during nighttime were relatively stable, ranging between -0.08 and 0.72 nmol m⁻² s⁻¹. In contrast, the daytime period exhibited a pronounced diurnal pattern characterized by a distinct maximum in the late morning hours. This behavior can be attributed primarily to the diurnal dynamics of turbulent exchange.

Ammonia fluxes were calculated using Monin–Obukhov similarity theory (MOST) based on vertical concentration gradients and micrometeorological parameters. For diagnostic purposes, an effective turbulent transfer coefficient (Kc) was derived such that 5F=KcΔCΔz where Kc represents the stability-corrected exchange coefficient obtained from the MOST framework rather than an independently fitted parameter.

The turbulent diffusion coefficient (Kc), calculated from 2 min averaged flux and concentration gradient data, demonstrated a clear diurnal course. During the nighttime period (16:00–03:00 UTC, zonal time is UTC+2), Kc averaged 0.06 m² s⁻¹, indicating suppressed turbulent mixing due to limited surface energy input. In contrast, daytime values increased substantially, reaching approximately 0.17 m² s⁻¹ (Fig. 2), reflecting enhanced convective turbulence under higher radiation and thermal forcing.

The concentration gradient exhibited a similar daytime maximum, and together with Kc, governed the diurnal evolution of ammonia flux. Fluxes peaked at approximately 09:00 (11:00 local time), followed by a local minimum around midday. This midday reduction may be consistent with commonly observed stomatal regulation phenomena.

Ammonia emission via plant stomata appears to be partially constrained during midday hours. Elevated temperature and high vapor pressure deficit increase transpiration demand, leading to transient plant water stress. In response, plants regulate stomatal aperture through abscisic acid (ABA)-mediated signaling, resulting in partial stomatal closure even under high irradiance conditions. Midday stomatal closure is primarily driven by high vapor pressure deficit and plant water stress (Oren et al., 1999), and stomatal regulation functions as an active, ABA-mediated control of photosynthesis (Flexas and Medrano, 2002).

Despite reduced turbulent exchange during nighttime, the concentration gradient remained small. This suggests that nocturnal ammonia emissions were limited, resulting in near-equilibrium conditions between the surface and the overlying air layer. Under such conditions, reduced mixing does not necessarily lead to concentration build-up, as the source strength is insufficient to generate a pronounced vertical gradient (Sutton et al., 1995; Nemitz et al., 2000).

In our study, as shown in Fig. 2, emission dominates during the daytime hours, with a maximum around noon, whereas during the nighttime it shows relatively constant, low values and occasionally shifts to deposition. When separated based on global radiation and photosynthetically active radiation, the mean emission was 3.11 nmol m⁻² s⁻¹ under Ig > 0 and PAR > 0 conditions, while during nighttime hours (Ig = PAR = 0) it was an order of magnitude lower, 0.448 nmol m⁻² s⁻¹.

The daytime dominance of ammonia flux has long been recognized. For example, Harper et al. (1983) reported that the daily NH₃ cycle was pronounced, with substantial emission during the day and small emissions or even deposition at night. During the summer season, soil surface temperature was the factor most strongly correlated with NH₃ flux. During the remainder of the year, evapotranspiration showed the highest correlation, although the increased midday flux was likely attributable to the parallel increase in soil temperature and wind speed. All of the main influencing factors are interrelated through their dependence on solar radiation.

In a review study, Hargrove (1988) listed several factors determining ammonia flux. Environmental variables such as temperature, soil moisture content, and air exchange at the soil surface are primary determinants of the magnitude of NH₃ loss. Soil moisture and surface air exchange are particularly important. Under field conditions, these factors fluctuate widely on a daily basis due to the combined effects of dew formation and evaporation. Studies cited in Hargrove (1988) indicate that, on a daily scale, high NH₃ loss rates are generally associated with periods of rapid soil drying, when moist (near field capacity) surface soil is followed by several days with little or no rainfall (< 1 mm). It is also evident that NH₃ loss is related to wind speed under field conditions, and that low air exchange rates at the soil surface – such as those expected within a plant canopy or in no-till production systems – may limit NH₃ loss.

Recent research has reinforced that ammonia emissions are strongly controlled by interactions among soil properties, meteorological conditions, and management practices. Advanced atmospheric emission models show that incorporating spatial and temporal variability in agricultural activities, such as manure and fertilizer application timing, as well as explicit representation of soil moisture and temperature, significantly improves simulation of observed NH₃ emission dynamics across Europe and beyond (Ge et al., 2020). Field and satellite-based studies further highlight that environmental drivers and atmospheric lifetime of NH₃ vary considerably with local conditions, affecting both emission rates and dispersion patterns (Xie et al., 2024). Reviews also emphasize the profound contribution of agriculture to global ammonia emissions and their impacts on particulate formation and human health, underscoring the need to account for complex environmental dependencies when estimating NH₃ fluxes (Wyer et al., 2022).

It is therefore clear that identifying the factors controlling emission is not straightforward, as their relative importance varies depending on the specific environmental conditions.

During the investigated period (4.662 × 10⁶ s), the mean ammonia emission was 1.85 nmol m⁻² s⁻¹, corresponding to a cumulative loss of 1.21 kg N ha⁻¹. Based on instrumental uncertainty (±2 ppb) and literature-reported uncertainty ranges of MOST-based aerodynamic gradient flux calculations, the overall uncertainty is estimated to be approximately ±25 %, corresponding to ±0.30 kg N ha⁻¹ when expressed as nitrogen, representing 4.0 % of the applied fertilizer nitrogen.

Emission dynamics were strongly time-dependent (Fig. 3). Immediately after fertilization, elevated fluxes were observed under bare soil conditions, reflecting high surface emission potential. In the following days, fluxes declined progressively, consistent with depletion of readily volatilizable ammonium and changes in soil-surface equilibrium conditions.

Superimposed on this seasonal-scale decay, pronounced short-term variability was observed, driven by diurnal changes in radiation and turbulent exchange as discussed in Sect. 3.2. The overall fertilizer-related nitrogen loss (4 %) falls within the lower range reported in the literature for similar mineral fertilizer applications under relatively dry soil conditions.

Synthetic nitrogen fertilizers are applied in various forms, including urea, ammonium nitrate, ammonium sulphate, calcium ammonium nitrate, UAN, and phosphate-based ammonium fertilizers (Amhamed et al., 2022). Following application, a portion of ammonium is taken up by plants or transformed through nitrification, while a significant fraction may be lost via gaseous emissions – particularly as NH₃, which typically peaks shortly after fertilization and can account for 6 %–20 % of applied nitrogen depending on fertilizer type, soil properties, climate, and management practices (Génermont and Cellier, 1997; Sommer et al., 2004; Zhan et al., 2020; Ma et al., 2021). Emission responses are strongly nonlinear and often increase exponentially with application rate (Jiang et al., 2017). Huang et al. (2017) reported that under mineral fertilizer treatments (NK/NP/NPK), total NH₃ volatilization losses were ≤ 4.2 % of the applied nitrogen, whereas substantially higher losses were observed under combined organic and mineral fertilization.

In the present study, di-ammonium phosphate (DAP) was applied at a moderate rate and compared to urea-based fertilizers its volatilization potential is generally lower; consequently, the expected NH₃ loss response is less pronounced even under nonlinear dose–response relationships.

Regarding the operational range of the measurement system, the upper measurable NH₃ loss is not primarily limited by the fraction of fertilizer nitrogen lost through volatilization. Substantially higher volatilization losses than those observed in the present study could in principle be quantified, provided that the NH₃ mixing ratios remain within the calibrated response range of the analyzer or are measured using appropriate dilution/calibration. Thus, the upper limit is determined by the instrumental linear range and sampling configuration rather than by the percentage loss of applied nitrogen itself.

The lower quantification limit is more difficult to define, because it depends on ambient NH₃ mixing ratios, the magnitude of the vertical concentration gradient, atmospheric turbulence, averaging time, and the duration of the integration period. For aerodynamic gradient measurements, the critical factor is the detectability of the vertical NH₃ concentration gradient rather than the absolute concentration alone. Based on the inter-channel uncertainty of approximately ±2 ppb and the estimated overall uncertainty of about ±0.30 kg N ha⁻¹ for the cumulative loss, seasonal NH₃ losses below approximately 0.3–0.5 kg N ha⁻¹ would become increasingly difficult to distinguish reliably from measurement uncertainty.

To further interpret the temporal variability of the measured NH₃ fluxes, an exploratory machine-learning analysis was performed using the observational dataset. The half-hourly NH₃ flux time series exhibited a pronounced diurnal cycle, a progressive decay trend, and strong short-term autocorrelation. Therefore, model validation was conducted using a strictly chronological (day-aware) split, with the first 80 % of days used for training and the remaining 20 % reserved for forward evaluation.

Models based solely on contemporaneous meteorological predictors showed negligible predictive skill (R2_test ≈ 0.01), indicating that instantaneous environmental drivers alone were insufficient to explain cross-day variability. Residual diagnostics revealed strong within-day persistence (lag-1 autocorrelation ≈ 0.33), motivating the explicit inclusion of autoregressive lag features up to six half-hour steps (3 h). Incorporating this short-term memory structure markedly improved predictive performance (R2_test ≈ 0.31) and reduced residual autocorrelation to near white-noise levels (lag-1 ACF ≈ 0.05). For the full dataset, inclusion of lag features increased predictive skill to R2_test ≈ 0.31. Subsequent regime-specific modelling further revealed distinct daytime and nighttime control structures.

In addition to the lagged-model analysis, the agreement between measured and model-predicted NH₃ fluxes was evaluated directly using the test subset. The predicted-versus-measured comparison showed a clear correspondence between the two datasets (Pearson r = 0.795, corresponding to r2 = 0.6322, n = 575) (Fig. 4).

Model interpretation revealed regime-dependent nonlinear controls. During daytime conditions (PAR > 0), radiation-related variables interacted strongly with autoregressive memory terms. ICE curves for NH₃_lag_1 under daytime conditions (Fig. 5) showed consistent positive persistence effects, while two-dimensional partial dependence surfaces (Fig. 6) indicated that the influence of prior flux state was amplified under high PAR. This pattern suggests radiation-modulated volatilization from a dynamically buffered surface reservoir, where energy availability enhances release efficiency conditional on recent emission history.

In contrast, nighttime conditions (PAR = 0) displayed a fundamentally different control structure. Radiation lost explanatory power, and turbulent transport metrics such as friction velocity (u*) and wind speed became dominant. ICE curves for u* (Fig. 7) revealed threshold-like behavior, with suppressed flux under weak turbulence and rapid increases once mixing intensified. Two-dimensional interaction surfaces (Fig. 8) confirmed that nighttime flux is primarily transport-limited, with strong nonlinear coupling between turbulence intensity and wind speed. Autoregressive memory remained relevant but interacted with mixing conditions rather than radiative forcing.

Together, these results demonstrate a clear regime shift between daytime and nighttime NH₃ exchange. Daytime flux is characterized by radiation-amplified persistence, whereas nighttime flux is controlled by turbulence-limited release. The temporal persistence represented by the 3 h lag window and the regime-dependent nonlinear interactions indicate that NH₃ emissions reflect a transient soil–surface reservoir modulated by environmental forcing rather than a purely instantaneous response. Chronological validation further highlights that ignoring temporal structure can substantially overestimate predictive skill. These analyses suggest that incorporating temporal persistence and regime-specific environmental controls may improve the interpretation of NH₃ flux dynamics.

Despite the inclusion of multiple soil, meteorological, and turbulence-related predictors, permutation importance consistently highlighted PAR and friction velocity (u*) as dominant controls. The compensation point concentration of the soil-plant system was not directly measured. The inferred reservoir behavior is consistent with, but does not directly quantify, soil–plant compensation point dynamics. Finally, regime-specific analyses were performed separately for daytime (PAR > 0) and nighttime (PAR = 0) conditions to identify potential shifts in dominant environmental controls. Separate tree-based ensemble models were fitted for the daytime and nighttime subsets to resolve regime-specific controls.