The Barro Colorado Island (BCI) site in Panama is located at 9.151° N, 79.855° W. It is a primary lowland (elevation 120 m) semi-deciduous tropical forest site with a mean canopy height of 30 m and few emergent trees (Cheng et al., 2022b; Detto et al., 2015; Detto and Pacala, 2022; Fang et al., 2022). It has distinct ?dry (mid-December to mid-April) and wet (late-April to early December) seasons (Ogden et al., 2013). The site exhibits a tropical monsoon climate (Am), characterized by a short dry season. The soils are mostly well weathered kaolinitic Oxisols. Meteorological and flux data were collected from a 45 m tower located on the top-plateau at a half-hour temporal resolution (Detto and Pacala, 2022). The mean annual precipitation, wind speed, air temperature, relative humidity, air pressure, shortwave radiation, and longwave radiation during 2015 to 2017 are 2025 mm, 2.94 m s⁻¹, 25.5 °C, 89 %, 98.8 kPa, 195 W m⁻², and 428 W m⁻², respectively (Table 1). The soil moisture is measured in the top 15 cm of the soil (Cheng et al., 2022b; Detto and Pacala, 2022).

The Pasoh Forest Reserve (PFR), known as the PSO AsiaFlux site, is a tropical forest located in Malaysia at 2.9667° N, 102.3° E. This lowland forest (140 m elevation) boasts a canopy height of 30–40 m, with emergent trees exceeding 45 m. The site is notable for being located within a dry zone of Peninsular Malaysia and receives the lowest annual rainfall among adjacent south-eastern tropical rainforests (Lion et al., 2017; Noguchi et al., 2016). The soils are dominated by Ultisols and Oxisols, which are Haplic Acrisol and Xanthic Ferralsol in FAO classification. The site has a tropical rainforest climate (Af), with consistently high rainfall throughout the year.

The observed data ?were measured at a height of 54 m on the flux tower at a half-hour temporal resolution (Lion et al., 2017). The mean annual precipitation, wind speed, air temperature, relative humidity, air pressure, shortwave radiation, and longwave radiation from 2003 to 2009 are 1790 mm, 1.86 m s⁻¹, 25.3 °C, 82.9 %, 98.9 kPa, 198 W m⁻², 419 W m⁻², respectively (Table 1). The volumetric soil water content is calculated as the average of observations from nine TDR (time domain reflectometry) sensors placed at depths of 10, 20, and 30 cm at three locations around the flux tower (Noguchi et al., 2016).

Figure 2 illustrates the algorithmic workflow of the proposed ML-based calibration framework, which integrates machine-learning-based emulation with a population-based global optimization algorithm to efficiently estimate optimal Noah-MP parameters while preserving the model's physical behavior. By replacing repeated expensive model evaluations with a fast emulator, the framework substantially reduces computational cost while maintaining accuracy and robustness.

The framework consists of two main steps. First, an ML-based emulator of Noah-MP is constructed to approximate the mapping from model parameters and meteorological forcing data to simulated land surface variables at each study site. For this purpose, we perform 1000 ensemble Noah-MP simulations using 1000 different parameter combinations sampled from Latin Hypercube Sampling and site-specific climate forcing. For each site, 80 % of these simulations are used to train the emulator, while the remaining 20 % are reserved for independent evaluation of emulator performance.

Second, the trained emulator is used to calibrate model parameters at each study site. Observational data are divided into calibration and validation periods. Parameters are optimized using observations from the calibration period only, and the optimized parameter set is then applied in full simulations with the original Noah-MP model over the entire study period. Model performance is evaluated separately for the calibration and validation periods using standard metrics. Details of the two-step calibration workflow, including emulator construction, evaluation, and calibration procedures, are described below.

We employ an Attention-Long Short-Term Memory (LSTM) neural network to construct the emulator, which is designed to capture the processes of the Noah-MP land surface model. LSTM networks are well suited for representing short- to medium-term temporal features (Kratzert et al., 2018), such as the memory of soil moisture states, while the attention mechanism further enhances generalization by dynamically weighting the importance of different historical time steps (e.g., antecedent precipitation events) when predicting current states.

The emulator learns a statistical approximation of Noah-MP behaviour, mapping model parameters and meteorological forcing data to simulated land surface states and fluxes. In this study, the emulator inputs consist of eight dynamic meteorological forcing variables, including 2 m temperature (T2M), rain rate (RAINRATE), longwave radiation (LWFORC), shortwave radiation (SWFORC), 2m specific humidity (Q2D), surface pressure (PSFC), 2 m U-wind component (U2D), and 2 m V-wind component (V2D), consistent with the parent Noah-MP model. In addition, nine model parameters, including both vegetation and soil parameters targeted for calibration (Table 2), are also provided as inputs.

The emulator is trained to predict a comprehensive set of 29 output variables (Figs. S3 and S4), including the three primary calibration targets, which are latent heat (LH), sensible heat (SH), and soil moisture (SM), as well as auxiliary diagnostic variables (e.g., ground heat flux, runoff components, and temperature states). Higher loss weights are assigned to the primary targets, while auxiliary variables act as process-aware constraints that respect the underlying conservation laws of energy and mass.

Training data for the emulator are generated data by sampling 1000 parameter combinations within prescribed bounds (Table 2) and running Noah-MP once for each parameter set, using identical site-specific forcing and model configuration. Each simulation produces time series of both primary target variables (LH, SH, and SM) and auxiliary variables (Figs. S3 and S4). The resulting dataset comprises 1000 paired samples of (θ,X1:T)→Y1:T, where θ denotes the parameter vector, X1:T the climate forcing, and Y1:T the Noah-MP simulated outputs. Because observational data are separated into calibration and validation periods for subsequent parameter calibration (Sect 2.5.3), emulator training uses the calibration-period forcing and the corresponding Noah-MP simulations. This dataset is subsequently split into training and evaluation subsets with an 80:20 ratio.

To prevent training instability caused by differing physical magnitudes, all input and output variables are standardized using Z-score normalization. The training loss aggregates weighted RMSE across all predicted variables, allowing the network to learn the coupled evolution of energy and water processes while accounting for differences in physical units. The loss function, Ltrain, is defined as: 1Ltrain=∑v∈Vwv×1N1T∑n=1N∑t=1Tx^v,n,t-xv,n,t2∑v∈Vwv=1,wv>0 where V represents the set of all emulator-predicted variables (29 variables in this study), N is the batch size (N=16 in this study), T is the total number of time steps, x^v,n,t and xv,n,i are normalized values of each variable from the emulator-predictions and Noah-MP-simulations, respectively, and wv is variable-specific weighting factor. Both x^v,n,t and xv,n,i are normalized values to account for disparate physical magnitudes across variables (e.g., W m⁻² for heat fluxes versus m³ m⁻³ for soil moisture) and to ensure numerical stability.

Before using the machine-learning-based emulator for parameter calibration, its predictive performance is assessed using the evaluation subset (20 % of ensemble Noah-MP simulations). Unlike the training loss (Eq. 1), emulator skill is assessed using denormalized outputs in physical units for each primary target variable (LH, SH, and SM).

The metrics of evaluating emulator performance include the coefficient of determination (R2, Eq. 2), root mean square error (RMSE, Eq. 3), and percent bias (PBIAS, Eq. 4). Only emulators demonstrating sufficient accuracy are used in subsequent calibration in Sect. 2.5.3, ensuring that parameter optimization is based on a reliable approximation of Noah-MP behaviour. 2R2=1M⋅∑m=1M1-∑t=1Tym,t-y^m,t2∑t=1Tym,t-ym-2,ym-=1T∑t=1Tym,t where y and y^ are original values of each variable from the emulator-predictions and Noah-MP-simulations, respectively, and M is the ensemble size used for emulator evaluation (20 % of the ensemble Noah-MP simulations in this study). 3RMSE=1M⋅∑m=1M1T∑t=1Ty^m,t-ym,t2 4PBIAS=1M⋅∑m=1M100⋅∑t=1Ty^m,t-ym,t∑t=1Tym,t+ε

To ensure the robustness of the calibrated parameters and assess their transferability to unseen temporal conditions, we separate the observational data into calibration and validation periods, conduct the calibration using only the forcing data and observations from the calibration period, and reserve the remaining independent and unseen data for subsequent validation. For the Panama BCI site, the calibration period is 30 July 2015 to 29 July 2016 and the validation period is 30 July 2016 to 30 July 2017. For the Malaysia PSO site, the calibration period is 1 January 2005 to 31 December 2006 and the validation period is 1 January 2007 to 30 December 2009.

Following the emulator construction and evaluation, parameter calibration is performed using the Differential Evolution (DE) algorithm (Storn and Price, 1997). DE is a population-based optimization method well suited to highly non-linear and non-differentiable objectives typical of land-surface model calibration.

Starting from an initial population sampled within parameter bounds, DE iteratively proposes new candidates through mutation and crossover operations and retains those that improve the objective function. In our implementation, DE iteratively generates populations of parameter vectors. For each candidate vector, the emulator predicts the corresponding model outputs which are then evaluated against in situ observations using the objective function defined in Equation 7. This objective function is formulated to minimize discrepancies between emulator-predicted fluxes and the observed fluxes. This cycle repeats until convergence criteria are met or the maximum number of generations is reached.

Multiple independent DE runs with different random seeds are conducted to reduce sensitivity to stochastic effects. This yields an ensemble of calibrated parameter sets, from which we report the best-performing solution. This multi-run design also provides a practical diagnostic of identifiability: parameters that consistently converge to similar values across independent runs are more likely to be well constrained by the data and objective.

Calibration is formulated as a joint optimization problem to explicitly account for interactions and trade-offs among energy and water fluxes. For each primary variable, RMSE is first computed in physical units over all valid (non-missing) time steps (Eq. 5) and then normalized by the observed dynamic range to obtain a dimensionless error (Eq. 6). The overall calibration loss is defined as a weighted sum of normalized RMSE across the three primary target variables (LH, SH, and SM) (Eq. 7). 5RMSEp=1T∑t=1Tz^p,t-zp,t2 where p is the primary target variable  LH, SH, or SM), and z and z^ are flux tower observations and Noah-MP-simulations, respectively. 6NRMSEp=RMSEpmaxzp-minzp+ε7Lcalibration=∑p∈Pwp×NRMSEp,∑p∈Pwp=1,wp>0 where P represents the set of primary target variables for calibration (LH, SH, and SM in this study), and wp is the variable-specific weighting factor.

This Lcalibration metric aggregates the errors of different variables by normalizing them, thereby resolving the issue of disparate physical magnitudes. The weighting factor wp allows for flexible prioritization of specific physical processes based on site-specific conditions or measurement reliability. For instance, if observed SH of the study site is suspected to be biased, lower weights can be assigned to SH to ensure the model prioritizes the more credible sources of guidance.

For parameters with prior knowledge, fixed values can be set manually before calibration to impose additional physical constraints. For example, at the PSO site, LAI is fixed at the field-observed value of 6.52 m² m⁻² rather than calibrated.

Because the emulator is an approximation, the calibrated parameters are validated by applying them in simulations with the original Noah-MP model. The calibrated parameter set is therefore used to rerun Noah-MP over the complete study period.

Model performance is evaluated separately for the calibration and validation periods using standard metrics computed in physical units, including RMSE, R2, and bias (BIAS; Eq. 8). Performance during the calibration assesses whether the emulator-based calibration identifies parameterizations that translate to the physical model, while performance during the independent validation period evaluates generalization and robustness. 8BIAS=1T∑t=1Ty^t-yt

Different model parameters exert distinct influences on energy and water cycling processes (Table 3). At the Panama BCI tropical forest site, we find that the most important parameter for LH and SH is the maximum rate of carboxylation at 25 °C (VCMX25) (Table 3). VCMX25 controls the photosynthesis rate and stomatal conductance, and thereby also plays a dominant role in regulating carbon assimilation and evapotranspiration. The calibrated VCMX25 value (114.6 µmol CO₂ m⁻² s⁻¹) is consistent with values reported for Panama BCI tropical forests in previous studies (Cheng et al., 2024b).

While VCMX25 modulates both heat fluxes primarily through its influence on LH, with corresponding effects on SH via surface energy partitioning, MAXSMC and REFSMC also play a key role in regulating LH and SH, as they determine the soil water storage available for plants to uptake. In addition, Z0MVT directly regulates above-canopy SH flux, which induces a latent heat response by cooling the land surface.

The calibration substantially improves SH simulation at the daily scale during both the calibration and validation periods, demonstrating the effectiveness of the calibrated parameters (Fig. 4, Table 4). Specifically, during the calibration period, the mean bias of SH decreases from 30.6 W m⁻² under the default parameterization to 17.4 W m⁻² under the calibrated parameterization. During the validation period, the mean bias of SH decreases from 34.9 to 19.0 W m⁻². However, this improvement comes with a trade-off in LH performance: over the full period, the mean bias of LH increases from 5.6 W m⁻² for the default parameterization to 19.7 W m⁻² for the calibrated parameterization, and R2 for LH decreases from 0.80 to 0.65 (Table 4). Nevertheless, the gains in SH are substantial, with mean bias decreasing by 44 % (from 32.7 to 18.3 W m⁻²) and R2 increasing from 0.63 to 0.84 over the full period. In addition, the R2 under the calibrated parameterization remains stable between the calibration (0.87) and validation (0.81) periods.

The calibrated parameters improve the simulation of daily soil moisture at the Panama tropical forest site during both the calibration and validation periods (Fig. 4, Table 4). During the calibration period, the mean bias decreases from -0.020 m³ m⁻³ for default parameterization to 0.006 m³ m⁻³ for calibrated parameterization, while during the validation period it decreases from -0.035 to -0.008 m³ m⁻³. Over the full period, the mean bias decreases from -0.028 to -0.001 m³ m⁻³. RMSE decreases by 16.9 %, from 0.059 to 0.049 m³ m⁻³, with reductions of 17.6 % during calibration and 16.7 % during validation. R2 values increase from 0.51 under the default parameterization to 0.67 under the calibrated parameterization, rising from 0.61 to 0.73 during calibration and from 0.40 to 0.59 during validation (Table 4).

Beyond the daily scale, Noah-MP effectively captures the seasonal and diurnal dynamics of surface energy and water fluxes (Fig. 5). Specifically, it captures the seasonal decline in LH (Fig. 5a) and soil moisture (Fig. 5e), as well as the corresponding peak in SH around April (Fig. 5a). However, the model does not fully capture the peak in soil moisture from September to November (Fig. 5e), consistent with its deficiencies in simulating daily soil moisture peaks during the wet season (Fig. 4f). The underestimated wet-season soil moisture may be caused by the deficiencies in subsurface water transport representation, such as the absence of preferential flow simulation in Noah-MP, which is known to govern seasonal sub-surface fluxes of water in tropical rainforests by rapidly transporting water downward (Cheng et al., 2017, 2018, 2019). Preferential flow paths generated by tree root penetration, termite activity, earthworm burrows, or other soil microporosity significantly alter the partitioning of water and energy, affecting not only runoff, but also water storage and plant water uptake in tropical forests. Therefore, their absence in Noah-MP could be an important source of structural error which would further hinder calibrations based on heat fluxes. This critical process has received insufficient attention in the context of land surface modelling and deserves future model development efforts.

The trade-off in optimizing LH and SH at the daily scale (Fig. 4) also persists at the seasonal and diurnal scales (Fig. 5). LH overestimation is most pronounced between January and April, as the dry season develops but simulated LH remains relatively high. We note from Fig. 4e and f that the dry down of soil moisture at these times of year is poorly captured, with both the calibrated and uncalibrated models overestimating soil moisture, which may contribute to LH biases. Additional factors include potential biases in downward solar radiation measurements from the flux tower. If it is overestimated, this could contribute to the overall overestimation of both latent and sensible heat fluxes.

Another possible source of the discrepancy between calibrated LH and SH may be Noah-MP's inability to simulate forest functional diversity, which are prevalent in tropical forests and critical for capturing forest response to environmental variability (Cheng et al., 2024b). Addressing this limitation may require the use of more advanced ecosystem demography models to better capture the interactions of multi-species coexistence in tropical ecosystems.

The model persistently overestimates nighttime SH (Fig. 5d), corresponding to overestimated nighttime soil temperatures (Fig. S5). This discrepancy likely stems from the absence of a soil organic layer parameterization in Noah-MP. Organic layers, with low thermal conductivity and high heat capacity, buffer both daytime heating and nocturnal cooling. Without this buffering effect, the model likely exaggerates diurnal soil temperature amplitudes, inflating both daytime peaks and nighttime minima. This structural limitation, recognized in previous evaluations (Zhang et al., 2021), contributes to systematic SH biases and highlights a priority area for future model development.

The single most important parameters for calibrating LH and SH at the Malaysia PSO tropical forest site are VCMX25 and WLTSMC, due to their roles in controlling photosynthesis and soil water availability (Table 5). Other soil parameters, including WLTSMC and SATDK, also strongly influence Noah-MP simulations of energy and water fluxes by regulating the amount of soil moisture available for plant uptake. LAI is prescribed based on site measurements rather than calibrated, but it is also important for both  H and SH due to its role in controlling vegetation phenology.

The calibrated parameters substantially improve the simulation of daily energy and water fluxes at the Malaysia PSO tropical forest site, during both the calibration and validation periods (Fig. 6, Table 6). Unlike the Panama BCI site, where improvements in latent and sensible heat exhibit a trade-off, calibration at the PSO site leads to simultaneous improvements in both fluxes. During the calibration period, the mean bias of LH decreases from -14.2 W m⁻² under the default parameterization to -8.4 W/m² after calibration, while mean bias of SH decreases from 7.6 to 3.3 W m⁻². During the validation period, mean LH bias decreases from -10.0 to -2.3 W m⁻², and mean SH bias decreases from 5.8 to -0.3 W m⁻². Over the full period, the mean bias of LH decreases from -11.7 to -4.7 W m⁻², and mean SH bias decreases from 6.5 to 1.2 W m⁻².

For soil moisture, the emulator-based calibration significantly outperforms the default configuration, particularly during the validation period. The default configuration exhibits reduced stability, with R2 decreasing from 0.62 during the calibration period to 0.51 during validation, while the mean bias increases from -0.009 to -0.014 m³ m⁻³. In contrast, simulations using calibrated parameter values perform better during the calibration period, achieving a lower RMSE (0.019 m³ m⁻³ compared to 0.022 m³ m⁻³ for default parameterization) and a higher R2 (0.73) than default parameterization (0.62). During the validation period, the calibrated configuration not only maintains its predictive skill but further improves, yielding the lowest RMSE of 0.015 m³ m⁻³ and a stable R2 of 0.74. Overall, calibration attempts can be considered more successful for PSO in Malaysia than for BCI in Panama, possibly because the weaker seasonality at the Malaysia site means that the models do not need to capture distinct wet-dry transitions.

In addition to daily dynamics, Noah-MP adequately captures both seasonal and diurnal dynamics of energy and water fluxes at the PSO site (Fig. 7). At the seasonal scale, both model configurations capture the decline in LH from April to July and from September to December (Fig. 7a and b). Calibration greatly improves the simulation of LH, by removing a substantial underestimate that is present for all months with the default parameters (Fig. 7a). SH is similarly improved, except between February and April, when the decrease in SH due to calibration leads to an underestimation; however, the seasonal dynamics from May to December are well captured and substantially improved relative to the default parameterization. Soil moisture shows weaker seasonal variability than at the Panama BCI site and is reasonably well captured by both the default and calibrated configurations.

At the diurnal scale, Noah-MP with calibrated parameterization better captures the peaks in LH (Fig. 7b) around noon time compared to default parameterization. These improvements indicate that calibration at the daily timescale translates into enhanced model performance at sub-daily scales. Interestingly, for SH, the peak of the diurnal cycle is underestimated after calibration, even though the overall performance on daily and seasonal timescales is improved. This stems from the period from February to April, when the calibrated SH values are further reduced relative to the default, resulting in greater underestimation compared to observations. The variation in model performance in capturing the diurnal cycle across seasons clearly reveals this contrast. Specifically, from February to April, calibration increases the SH mean bias from +1.1 W m⁻² (default) to -6.6 W m⁻². While in the remaining months, calibration reduces the mean bias from 8.2 W m⁻² (default) to 0.02 W m⁻².

The notable success of co-calibration of both heat fluxes at PSO in Malaysia, compared to the conflicting results for LH and SH at BCI in Panama, is perhaps due to the large differences in climate and vegetation conditions between the two locations. Specifically, Panama has a tropical monsoon climate (Am), characterized by distinct dry and wet seasons, while Malaysia experiences a tropical rainforest climate (Af), with consistently high rainfall throughout the year. Furthermore, despite receiving less rainfall, the PSO site exhibits higher LH than the BCI site (Table 1), suggesting that structural vegetation differences, such as LAI (represented at PSO by the sensitivity of the model to LAI) and canopy wind effects, are playing a significant role in energy fluxes. For example, the positive LH biases at PSO with default parameters may be partially a result of underestimated damping of in-canopy winds by the relatively denser canopy, in which case calibrating LAI and CWPVT can be expected to improve both LH and SH. As a result, the parameters are not transferable between the two sites.

Noah-MP's inability to simulate the coexistence of multiple tropical forest species may contribute to discrepancies between calibrated LH and SH. Tropical forests are characterized by high biodiversity, including species with varying ages, sizes, and functional traits. These factors are essential for accurately representing energy, water, and carbon cycling as well as ecosystem functions (Cheng et al., 2024b). Incorporating more advanced ecosystem demography models into Noah-MP would allow for better simulation of these ecosystem dynamics. Additionally, the absence of an organic soil layer can contribute to the model's overestimation of nighttime soil temperatures, highlighting another important area for future development.

The absence of preferential flow pathways, which are formed by tree roots and earthworm burrows, is another likely source of structural error in Noah-MP. These pathways are prevalent in tropical regions and play a crucial role in rainfall partitioning and hydrological responses (Cheng et al., 2017, 2018). Their exclusion may undermine model calibration efforts for surface heat fluxes. Despite their importance, these processes remain underrepresented in land surface models and should be prioritized in future model improvement efforts. Macropores can be characterized by their size and number, and their distributions are commonly described using normal or log-normal functions (Edwards et al., 1988; Munyankusi et al., 1994; Cheng et al., 2017, 2018). The volumetric flow rate within an individual macropore can be calculated using Poiseuille's law for pipe flow (Sutera and Skalak, 1993; Cheng et al., 2017, 2018). This information provides a basis for future model development efforts to incorporate preferential flow pathways into Noah-MP.