Monthly mean air temperature (Ta), relative humidity (RH), and zonal, meridional, and vertical wind components were obtained from the ERA5 reanalysis dataset . These data were utilized for the period 1981–2025 across 27 vertical pressure levels ranging from 1000 to 100 hPa, with a spatial resolution of 0.25°. Monthly SST from ERA5 was also utilized to provide context for the identified extreme hydroclimatic events. The SST data from the ERA5 reanalysis – which strictly prescribes observation-based products such as HadISST2 and OSTIA – were used to characterize the oceanic boundary conditions. The use of ERA5 SST, rather than an independent observational product, ensures strict thermodynamic consistency, as it represents the exact surface forcing that generated the atmospheric response (ω and ΔT) evaluated in this study.

To validate the proposed climate index, two independent high-resolution precipitation products developed specifically for the complex Peruvian topography were employed. First, the RAIN4PE product was used for the 1981–2015 period. RAIN4PE is a gridded dataset that merges three data sources – satellite estimates (CHIRPS), reanalysis data (ERA5), and ground observations – corrected via quantile mapping and validated through hydrological modeling to ensure consistency with observed streamflow and water balance closure. Second, the PISCO product (Peruvian Interpolated Data of the SENAMHI's Climatological and Hydrological Observations) was used for the 1981–2025 period. PISCO is a hybrid product developed by the National Meteorology and Hydrology Service of Peru (SENAMHI) that combines quality-controlled rain gauge records with satellite covariates (CHIRPS) using geostatistical interpolation techniques to reconstruct rainfall fields over data-scarce regions. It is important to note that the stable version of PISCO, which incorporates both manual and automatic quality control , is available only for the 1981–2016 period; consequently, the unstable version, which undergoes only automatic quality control, was utilized for the 2017–2025 period.

Monthly precipitation from ERA5 was used to identify the area within the NWSA exhibiting the highest similarity with observational datasets, given that the proposed index is constructed entirely from ERA5 variables. Figure shows that ERA5 is significantly correlated with RAIN4PE and PISCO over the entire domain, being strongest near the coast between Peru and Ecuador. This high correlation along the coastal strip is primarily due to large-scale synoptic and dynamic boundaries that global reanalyses effectively resolve, coupled with a high density of meteorological stations that enhances the reliability of PISCO and RAIN4PE in this specific subregion .

Conversely, the correlation weakens significantly over the Andes and the Amazon basin. Over the Andes, ERA5’s spatial resolution is too coarse to adequately capture fine-scale orographic precipitation, systematically leading to overestimations . In contrast, regional gridded products mitigate this by incorporating local terrain elevation models and dense gauge networks. Over the Amazon basin, precipitation is largely driven by localized mesoscale convective systems and intense moisture recycling , which remain challenging for ERA5's convective parameterizations to simulate accurately. This physical discrepancy is further compounded by the sparse distribution of rain gauges in the Amazon, which sharply increases the spatial interpolation uncertainty in observation-based datasets .

Furthermore, to evaluate the prognostic utility of the BWR index, predicted atmospheric variables and direct precipitation outputs were obtained from the fifth generation of the ECMWF seasonal forecasting system (SEAS5) . SEAS5 is an operational coupled global climate model designed for long-range predictions. Given the inherent uncertainty and chaotic nature of seasonal forecasting, this study specifically utilizes the monthly ensemble means of the real-time forecasts rather than individual deterministic members. This approach filters out high-frequency internal variability, isolating the predictable macro-scale signal required for the BWR calculation. The forecast data spans the operational period from 2017 to 2025.

Two domains of interest were defined: the broader NWSA region (81.6–67.05° W, 18.95° S–1.5° N) and a specific coastal subdomain adjacent to the Niño 1+2 region (81.25–78.5° W, 8° S–0.75° N) (Fig. ).

The coastal subdomain NWSA (Fig. b) is typically located under the regional branch of the Walker circulation, characterized by persistent subsidence and trade-wind-driven coastal upwelling that suppresses convection. This stability is reinforced by the mid-level easterly flows, which, upon crossing the Andes, descend, forcing a dry leeward subsidence on the coastal strip , but this subsidence weakens during the short austral summer. However during El Niño events, this subsidence regime collapses: the South Pacific Anticyclone migrates southward, upwelling weakens, and warm sea surface temperatures (SST) invert the low-to-mid-level flows into anomalous westerlies below 5 km , generated by the sea breeze colliding against the western Andean slope . This westerly moisture advection around 600 hPa becomes essential to organize convective systems and couple them with the second band of the ITCZ , while low-level sea breezes force windward orographic ascent that helps air parcels reach their level of free convection . Physically, this dynamically limited region operates as a thermodynamic switch governed by Strict Quasi-Equilibrium (SQE) dynamics: during dry months, the SQE is decoupled and net vertical motion (ω) fluctuates without producing rain; but once the SST exceeds the critical ∼26 °C threshold , the inversion breaks and the system enters a rigidly coupled SQE regime, where ω and the latent heat of precipitation feed each other in a contemporaneous, bidirectional loop .

Figure presents the precipitation climatology (1981–2025) from PISCO averaged over this coastal subdomain. It is observed that March constitutes the rainiest month; this seasonal peak represents a critical coupling window when dynamic relaxation (weakening of trade winds) and atmospheric instability (SST warming) come into phase, facilitating the development of deep convection .

To characterize the distinct vertical atmospheric configurations associated with extreme hydroclimatic anomalies, a set of representative case studies was identified. Monthly precipitation was averaged over the coastal NWSA subdomain (Fig. b), and anomalies were calculated from the PISCO dataset relative to the 1981–2015 climatological mean. Two thresholds, corresponding to the 5th and 95th percentiles, were defined solely for event selection purposes: anomalies below 5th percentile were used to detect significant dry events, and anomalies above 95th percentile were used to detect extreme rainy events. It is important to clarify that these thresholds were applied exclusively to select events for physical diagnosis (e.g., analyzing vertical structure) and were not utilized to calibrate or derive the formulation of the proposed index. To determine the spatial core of these anomalies, the vertical motion field was analyzed through latitudinal and longitudinal cross-sections (see Figs. and in Sect. ). The longitude of 80° W and latitude of 5° S were identified, approximately, as the axes of maximum vertical ascent over the coastal subdomain. This geometric characterization allowed for the identification of subsidence and convective layers, as well as the specific pressure levels where convection was initiated and suppressed during the selected case studies.

The formulation of the BWR is physically grounded in the thermodynamic energy balance of the Walker circulation described by , which posits that on climatic timescales, latent heat release is primarily balanced by adiabatic cooling due to vertical motion. Consequently, an index capable of explaining precipitation anomalies in this region must explicitly couple the atmospheric instability with the dynamic forcing (vertical velocity) required to overcome the persistent background subsidence.

First, the dew point temperature (Td) was calculated from relative humidity following . Using surface Td and air temperature (Ta), the parcel temperature path was computed and compared against the environmental temperature profile to yield the parcel buoyancy (ΔT) for every grid point. To construct the index, the product of vertical velocity (ω) and parcel buoyancy (ΔT) was analyzed. The Buoyancy Work Rate (BWR) is defined as the vertical integration of this product from the surface to 100 hPa with respect to the natural logarithm of pressure (dln⁡P), as shown in Eq. (). 1BWR=-∫sfc100ωΔTdln⁡P In this integration, only layers exhibiting positive buoyancy (ΔT>0) and upward motion (ω<0) were included. This constraint ensures that the index specifically quantifies the rate at which potential energy is converted into kinetic energy during deep convection, filtering out stratiform or forced ascent in stable environments.

To understand this diagnostic formulation, it is instructive to mathematically and conceptually contrast the BWR with CAPE. CAPE is defined as the vertical integral of parcel buoyancy from the level of free convection to the equilibrium level . It strictly evaluates the precursor thermodynamic potential energy available for convection, remaining mathematically blind to whether a dynamic trigger actually exists to overcome background subsidence . In contrast, the BWR is formulated by integrating the product of thermodynamic instability (ΔT) and vertical velocity (ω) across the atmospheric column. Rather than measuring stored static potential, this hybrid formulation explicitly quantifies the realized rate of kinetic energy conversion. By mathematically coupling buoyancy with mesoscale kinematic ascent, the BWR imposes a strict physical constraint: it systematically penalizes and zeroes out environments that possess massive thermodynamic instability (high CAPE) but remain mechanically suppressed by persistent subsidence (ω>0).

To evaluate the physical robustness and predictive utility of the BWR, a multi-tiered validation framework was implemented, moving from causal verification to statistical comparative evaluation.

To quantify the skill of the BWR relative to established indices, the spatial distribution of the Pearson correlation coefficient (R) was analyzed (Fig. ). A clear spatial divergence emerges: while CAPE, GDI, and the BWR all exhibit positive correlations over the NWSA, the BWR and CAPE display stronger correlations than the GDI in the coastal subdomain (Fig. b). However, their performance diverges significantly over the Amazon basin and eastern Andes. In these continental regions, the GDI maintains slightly higher positive correlations than the BWR, whereas CAPE collapses, exhibiting non-significant or significantly negative correlations.

This divergence reflects the fundamental physical differences in how each index interacts with varying convective regimes. Along the dynamically limited coastal region, deep convection is a rare, binary process governed by large-scale subsidence. When this dynamic suppression relaxes and coincides with local surface warming, the boundary layer rapidly destabilizes . Because coastal precipitation is strictly governed by this synchronized activation of surface instability and dynamic lifting, the BWR and CAPE capture the convective variance more accurately than the GDI, whose heavy reliance on mid-tropospheric moisture makes it slightly less sensitive to the boundary-layer triggers of this specific regime.

Conversely, the Amazon basin and eastern Andes constitute a thermodynamically abundant regime governed by Mesoscale Convective Systems (MCS), orographic lifting, and intense local moisture recycling . Here, CAPE systematically fails because it evaluates raw potential energy. As demonstrated by , maximum instability occurs during the spring transition, when intense surface heating generates high CAPE, but convection is suppressed by Convective Inhibition (CIN). During the peak wet season, extensive cloud shading and convective consumption actively destroy this instability despite high precipitation volumes . This out-of-phase relationship generates the negative correlations for CAPE at the monthly timescale. In contrast, the GDI and BWR remain positively correlated because they do not rely solely on raw buoyancy. The GDI incorporates mid-tropospheric moisture, which remains persistently high during the rainy season, giving it a slight diagnostic advantage over the continent. While the BWR is rescued from the thermodynamic phase-shift by its vertical velocity (ω) component, its correlation is slightly weaker than the GDI over the eastern Andes. This physically occurs because the macro-scale ω cannot fully resolve the fine-scale orographic lifting or the localized MCS dynamics that dominate Andean precipitation, whereas the GDI's moisture fields provide a more continuous spatial proxy in complex terrain.

Focusing on the critical coastal subdomain (Fig. b), the standardized scatterplots (Fig. ) reveal that the BWR achieves the highest linear association and lowest dispersion among all evaluated indices. Unlike Ia and Id, which show little relation to the intensity of anomalies, the BWR scales proportionally with precipitation magnitude. While the BWR calculation requires surface dew point temperature (Td), which is tightly constrained by local oceanic boundary conditions (e.g., Niño 1+2 SST), the GDI fundamentally requires mid-tropospheric humidity . This distinction is critical because free-tropospheric moisture is highly sensitive to sub-grid convective parameterization schemes and remote advection, leading to substantial inter-model spread and systematic biases in climate models . Unlike surface and boundary-layer variables, whose variance is physically anchored by local SSTs via the Clausius-Clapeyron relationship , mid-level humidity in climate models inherits significant uncertainty. Consequently, metrics dependent on free-tropospheric moisture could inherit more uncertainty for climate monitoring compared to surface-constrained proxies.

The temporal evolution of the indices (Fig. ) highlights specific strengths. The BWR outperformed other indices in capturing the magnitude of the extreme 1983 and 1998 El Niño events. For the 1998 event, the index aligned closely with precipitation observations, helping to resolve discrepancies between PISCO and RAIN4PE products. In the recent 2023 Coastal El Niño, all indices and ERA5 precipitation peaked in March–April; however, the PISCO product exhibited a sudden and physically unexplained decline in April. To validate the positive anomalies diagnosed by the BWR and ERA5 during this period, independent official climatological reports were consulted. Specifically, the National Meteorological and Hydrological Service of Peru and the Ministry of Agriculture and Livestock of Ecuador documented significant positive rainfall anomalies along the northern Peruvian and southern Ecuadorian coasts during April 2023. Furthermore, during the 2024 dry event, PISCO showed a contradictory positive anomaly peak in April, whereas BWR, CAPE, and ERA5 precipitation consistently indicated negative anomalies according with observational monthly reports . This independent observational consensus supports the physical consistency of the BWR, highlighting its value as a robust diagnostic tool.

Figure a presents the reference causal network, constrained by the physical link assumptions described in Sect. . Although the causal directionality was a priori imposed to break the simultaneous circularity, the algorithm quantified the strength of these conditional dependencies. Such as, the SST over Niño 1+2 and the mesoscale vertical velocity (-ω500) exert a strong control over atmospheric instability (ΔT700-400) [MCI: 0.73] and precipitation [MCI: 0.61], respectively.

Building upon this reference, the second causal network (Fig. b) illustrates the system after the introduction of the BWR index. The resulting causal network confirms the preservation of the mesoscale thermodynamic and dynamic signals governing precipitation. Most importantly, the BWR index maintains a direct, robust causal link to precipitation [MCI: 0.60, with a confidence of 95.9 %] that exceeds the local evaporation signal [MCI: 0.25, with a confidence of 81.1 %]. This indicates that although local evaporation provides the necessary moisture for initial cloud formation, mid-level moisture advection plays a critical role in maintaining deep convection, and even helping to form the secondary band of the ITCZ , by mitigating the drying effect of environmental air entrainment and slowing down cloud evaporation . Consequently, this validates the BWR formulation as a coherent physical integrator that couples the dominant dynamic with the thermodynamic, preserving the causal route to precipitation with significant strength [MCI: 0.60], even when the individual variables are algorithmically abstracted into the vertically integrated index (BWR).

To characterize the atmospheric conditions associated with extreme hydroclimatic anomalies, March precipitation anomalies were analyzed over the coastal subdomain (Fig. ). Based on the thresholds defined in Sect. , the rainiest (1983, 1993, 1998, 2002, 2017, 2022, 2023, and 2025) and driest (1982, 1985, 1988, 2003, 2011, and 2018) events were identified. As established in previous studies, these extreme precipitation responses are fundamentally governed by coastal El Niño and La Niña events, evidenced by SST anomalies in the Niño 1+2 region (Fig. ). Within this set, the 1998 and 2017 events are of particular interest as they encompass distinct oceanic dynamics driving similar precipitation extremes: while 1998 represents a canonical basin-wide extreme El Niño , 2017 manifested as a highly localized extreme coastal El Niño, characterized by intense warming strictly confined to the far-eastern Pacific despite weak La Niña conditions in the central basin . Additionally, the 2016 event was included as a contrasting case study because, despite prevailing strong global El Niño conditions, it lacked an extreme hydroclimatic response along the coast compared to the 1983 or 1998 events . This deviation underscores the notable influence that internal atmospheric variability can exert in altering regional teleconnections during distinct El Niño flavors .

To rigorously evaluate the robustness of the BWR during critical hydroclimatic phases, an Upper Tail Dependence (λU) analysis was conducted using empirical copulas. This approach quantifies the conditional probability that precipitation exceeds a high quantile given that the predictor index also exceeds the same quantile, providing a measure of asymptotic dependence essential for risk assessment. The copula space visualization (Fig. , left) exhibits a cross-like structure. While the main diagonal confirms the primary physical coupling, the anti-diagonal reveals regime mismatches in moderate conditions (e.g., false positives). However, the λU analysis (Fig. , right) demonstrates that this noise fades in the extremes. The λU coefficient increases for higher quantiles, peaking near 0.8 at the 97.5th percentile. This confirms strong asymptotic tail dependence: while the index may produce noise during moderate anomalies, it becomes a highly reliable diagnostic proxy specifically for the most extreme, potentially disastrous precipitation events.

While large-scale dynamic ascent (ω500) alone might dictate instantaneous extremes, its utility for continuous monitoring is limited by its chaotic nature. This was assessed through a signal persistence analysis (Fig. ). A rapid decorrelation was observed for ω500 (blue line), which loses significant memory after short lags. In contrast, by integrating ΔT, the BWR (green line) mathematically inherits the thermal inertia of the oceanic boundary conditions. This integration effectively “anchors” the volatile dynamic signal to the slower-evolving thermodynamic state, yielding a predictability horizon significantly longer than that of pure ω500. Thus, the BWR represents a physical trade-off: it sacrifices a marginal fraction of diagnostic precision at the extreme tail (compared to pure ω) to gain substantial signal stability and predictive capability, rendering it a highly practical tool for sub-seasonal to seasonal operative monitoring.

During the peak of the rainy season (February–April), BWR anomaly predictions initialized in November and December exhibit a consistent improvement in predictive skill (ΔR≈0.1 to 0.2) compared with precipitation anomalies predicted by the ECMWF SEAS5 model (Fig. ). Predicting precipitation anomalies in the NWSA during this critical hydroclimatic period is inherently complex due to the interaction between large-scale moisture convergence and the steep Andean topography . Climate models often exhibit significant biases in these dynamically limited regimes because they rely on sub-grid convective parameterizations to generate local precipitation . By substituting direct precipitation outputs with the BWR, the diagnosis circumvents these microphysical uncertainties. Instead, the BWR leverages the explicitly resolved large-scale vertical dynamics (ω) and thermodynamics (ΔT), which are governed by primitive equations and simulated with substantially greater fidelity by models .

Furthermore, the BWR demonstrates a significant advantage for extended-lead predictions initialized in May, targeting the austral spring (October–November). At these 5- to 6-month lead times, the BWR anomalies yield marked correlation improvements (ΔR>0.3). This indicates that the BWR effectively retains predictive skill across the boreal spring predictability barrier. Because the BWR integrates the mesoscale atmospheric energetic conversion rather than relying on parameterized local rainfall, it provides a more robust and persistent proxy for the atmospheric state, confirming its operational utility for sub-seasonal to seasonal forecasting.

The causal networks evaluated in Sect.  empirically support the physical hierarchy preserved by the BWR index, whose causal route to precipitation significantly dominates over other variables. This dominance is explained by the background dynamics of the region: although it is well established that local SST must exceed a specific threshold to trigger atmospheric instability , in dynamically limited environments such as the coastal subdomain, this atmospheric instability (ΔT) is a necessary but insufficient condition for deep convection . Once the thermodynamic threshold is surpassed, control shifts predominantly to the mesoscale vertical velocity (ω) . Specifically, convection requires a mechanical trigger, such as the localized vertical ascent generated by the sea breeze colliding against the western Andean slope . This forced ascent lifts the air parcel to its Level of Free Convection (LFC), initiating latent heat release. Consequently, mid-level ω emerges to balance this diabatic heating through adiabatic cooling , which, dictated by mass continuity, stimulates further low-level horizontal convergence, generating a circular causality known as convergence feedback . By mathematically abstracting this dynamic mechanism, the BWR acts as a coherent physical integrator that successfully couples vertical velocity with atmospheric instability without losing the causal route to precipitation.

The BWR index mathematically abstracts this exact dynamic mechanism to operate in the dynamically limited environment of the coastal subdomain through the product of -ω and ΔT. This mathematical formulation acts as a physical constraint: the bidirectional feedback is only quantitatively realized when dynamic ascent (-ω>0) coincides with thermodynamic instability (ΔT>0). If the atmospheric column remains mechanically suppressed by the background subsidence (ω>0), the index zeroes out values, explicitly capturing the inability of local buoyancy to autonomously initiate the convective feedback loop.

The interaction between this thermodynamic potential and its dynamic realization fully explains the divergent regional responses observed during different El Niño flavors. While SST controls atmospheric instability, while SST gradients drive low-level horizontal convergence . However, there are situations characterized by spatial and extensively homogeneous high SST values across the Pacific but with low SST gradients. This configuration translates into weak or null local convergence, as absolute high SSTs alone cannot force deep convection without the vertical ascent provided by spatial gradients (e.g., the 2015–2016 El Niño). Conversely, asymmetric or high SSTs confined over smaller areas, such as the Niño 1+2 region (e.g., the 2017 and 2023 coastal El Niño events), generate strong SST gradients that, initially, result in weak convergence, but when the convergence feedback is activated the convergence becomes stronger , seamlessly converting thermodynamic potential into the extreme hydroclimatic anomalies physically diagnosed by the BWR.

In dynamically limited environments like the NWSA coast, relying exclusively on thermodynamic indices yields high false-positive rates. As established by , thermodynamic instability (ΔT) is a necessary but insufficient condition for deep convection. When the regional Walker circulation imposes persistent subsidence, the atmospheric column remains mechanically suppressed despite intense surface warming. By mathematically coupling the thermodynamic potential with the vertical velocity (ω), the BWR acts as an explicit physical filter. It systematically zeroes out or yields negative values in thermodynamically unstable but dynamically suppressed environments, providing a selective diagnosis that purely thermodynamic predictors fail to capture .

Furthermore, the BWR provides diagnostic capabilities that extend beyond observing precipitation anomalies. In atmospheric fluid dynamics, the conversion of available potential energy to kinetic energy requires the ascending of warm air and the descending of cold air. For the NWSA coast, this conversion mechanism has been specifically documented within the Lorenz energy cycle framework by . By computing the product of temperature anomalies (ΔT) and vertical ascent (-ω), the BWR functions as a direct two-dimensional proxy for this three-dimensional energy conversion. Therefore, the BWR explicitly quantifies the intensity of the convective forcing engine, whereas precipitation merely records the subordinated thermodynamic output.

Further, while the mid-level vertical velocity (ω) ultimately dictates the convective outcome, its high-frequency variability and rapid decorrelation limit its utility as an isolated monitoring index. The NWSA coastal climate is strongly constrained by the SST, which evolves slowly due to the ocean's large heat capacity and acts as a boundary condition for deep convection . By integrating ΔT, the BWR mathematically inherits this oceanic thermal inertia. The resulting hybrid index retains the rigorous dynamic constraint of ω required to prevent false positives, while acquiring the temporal stability of the oceanic forcing, making it an optimal proxy for sub-seasonal operative monitoring.

Finally, beyond its diagnostic utility, the operational advantage of the BWR becomes evident when applied to climate models for seasonal predictions. In topographically complex regions like the NWSA, climate models systematically exhibit biases because they rely on sub-grid convective parameterizations to estimate localized precipitation . By substituting native precipitation outputs with the BWR, the forecast circumvents these microphysical uncertainties. The index evaluates the large-scale vertical dynamics (ω) and thermodynamics (ΔT), which are governed by primitive equations and explicitly resolved with higher accuracy by the models . Consequently, the BWR retains predictive skill at extended lead times and mitigates the forecast degradation caused by the boreal spring predictability barrier. By calculating the mesoscale atmospheric energy conversion rather than relying on parameterized rainfall, the BWR provides a physically robust proxy for operational predictions.

It is acknowledged that the BWR, in its current formulation using vertical velocity (ω in Pa s⁻¹), does not possess strict units of power density (W m⁻²). However, its mathematical formulation (-ωΔT) is directly proportional to the generation term of Kinetic Energy (KE) from Available Potential Energy (APE) in the Lorenz energy cycle . By capturing the upward motion of warm air and the downward motion of cold air , the index functions as a kinematic quantification of the energy conversion rate within the atmospheric column.

Despite the robust performance of the BWR during extreme events, significant limitations exist in moderate convective regimes, as evidenced by the dispersion observed in the copula space (Sect. ). These limitations stem directly from the index's simplified formulation. First, the BWR lacks an explicit humidity term. The index assumes that the product -ωΔT leads to latent heat release (Q), consistent with the tropical energy balance where Q is primarily balanced by adiabatic cooling . However, in cases of “dry ascent”, where strong dynamic lifting occurs in a moisture-starved environment, Q is limited by moisture availability rather than vertical motion. Consequently, the BWR yields false positives, measuring the intensity of the circulation's “engine” but not the efficiency of its output. Second, because the BWR is integrated from the surface to 100 hPa to strictly isolate deep convection, it systematically generates false negatives for precipitation driven by shallow convection or warm rain processes, which do not involve deep tropospheric ascent. Third, the current formulation lacks a high-frequency spatial filter. At native grid resolutions, the ω field inherently convolves the large-scale background dynamics with localized kinematic responses. While filtering the smaller horizontal scales in ω would isolate the large-scale environment to formulate a more transparent metric of precursor conditions leading eventually to precipitation anomalies, the current unfiltered index operates fundamentally as a diagnostic proxy of the realized convective state. Future efforts to further optimize the BWR will explore the application of spatial filters to the ω field.

Consequently, the translation of the BWR to other tropical latitudes imposes strict physical boundaries. Over continental regimes like the Amazon basin (Fig. ), deep convection is primarily constrained by convective inhibition (CIN) . Because the BWR evaluates dynamic forcing and positive buoyancy without accounting for the energy required to overcome CIN, its diagnostic correlation decreases significantly in these environments. Furthermore, over the eastern slopes of the Andes, precipitation is frequently driven by localized mechanical orographic lifting under conditions of weak large-scale ω . These highly localized mechanical processes are unresolved at the spatial resolution of current global reanalysis data , which physically exacerbates the generation of false negatives.

Beyond the tropics, the application of the BWR becomes physically inconsistent. In the midlatitudes and subtropics, atmospheric dynamics are predominantly governed by baroclinic instability, frontal lifting, and strong Coriolis forcing . Applying the BWR directly to extratropical regimes misrepresents the fundamental energy conversion processes driving precipitation in those latitudes. Finally, it must be reiterated that the BWR is fundamentally a diagnostic proxy of the macro-scale convective environment, not a direct measure of precipitation physics. The Tail Dependence analysis confirms that while the index's simplified formulation introduces noise during moderate conditions, these limitations become secondary during extreme events, where intense dynamic forcing and boundary-layer instability strictly dominate the atmospheric response.