the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 25 Mar 2026
Explaining monthly precipitation anomalies in northwestern South America by integrating vertical dynamics and energetics
Abstract. Northwestern South America (NWSA) is a critical region for monitoring El Niño-driven hydroclimatic extremes, receiving its maximum cumulative precipitation in March. Thermodynamic indices alone often fail to explain observed precipitation anomalies in this region because they neglect the limiting role of large-scale environmental dynamics. To bridge this gap, a diagnostic proxy called the Buoyancy Work Rate (BWR) is proposed, which quantifies the rate of conversion from potential to kinetic energy by coupling local thermodynamic instability (ΔT) with vertical motion (ω) forced by large-scale dynamics. The BWR is calculated by vertically integrating the product -ωΔT from the surface to the 100 hPa level. Using the PCMCI+ causal discovery algorithm, this study empirically validates the classical thermodynamic energy balance mechanism, demonstrating that precipitation in the NWSA is dynamically controlled, with ω exerting a causal influence significantly stronger than local evaporation. Validation via Tail Dependence analysis (λU) reveals that the BWR achieves robust asymptotic dependence (λU ~0.8) during extreme events. This robustness confirms the index’s ability to filter out thermodynamic false positives (e.g., the 2016 event) by incorporating the vertical velocity constraint. Furthermore, autocorrelation analysis indicates that the inclusion of the thermodynamic component imparts significant signal persistence to the index, stabilizing the inherently chaotic nature of pure vertical velocity. Physically, the index explains how dynamic forcing modulates precipitation outcomes across events with similar instability, resolving the contrasting impacts of the 2016, 2017, and 2023 El Niño events. Consequently, the BWR emerges as a physically consistent tool that offers a longer predictability horizon for monitoring sub-seasonal hydroclimatic risks.
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RC1: 'Comment on egusphere-2026-1049', Anonymous Referee #1, 09 Jun 2026
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AC1: 'Reply on RC1', Jose Obregon-Yataco, 10 Jun 2026
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We sincerely thank you for your positive feedback highlighting that our study is logical, well-organized, and presents the Buoyancy Work Rate (BWR) as a physically grounded predictor for sub-seasonal hydroclimatic extremes in NWSA. Below, we address each of your comments.
Point 1(1) Comment from referee: Precipitation and ascending motion are closely coupled, each influencing the other in a two-way interaction. In particular, latent heat released during precipitation formation warms the surrounding atmosphere and promotes local upward motion. Conversely, ascending motion creates favorable dynamical conditions for moisture condensation and precipitation development. The authors should clarify whether the interaction between precipitation and upward motion may influence the applicability of BWR over the NWSA.
(2) Author's response: We sincerely thank you for this insightful comment. We completely agree that on high-frequency (weather) timescales, precipitation and vertical motion are tightly coupled through a two-way interaction, where latent heat release warms the column and enhances local upward motion. However, we argue that this two-way interaction does not limit the applicability of the Buoyancy Work Rate (BWR) index over the NWSA due to the climatic timescale of our study and the macroscopic nature of the index.
We base this conclusion on two main arguments:
- Theoretical perspective (Temporal Scales and Energy Balance): While atmospheric dynamics and latent heat feedbacks occur on high-frequency timescales, our study focuses strictly on monthly averages to isolate robust climate signals. Based on the thermodynamic energy balance framework proposed by Cornejo-Garrido and Stone (1977) for the Walker circulation, the latent heat released from condensation on climate timescales is approximately balanced by adiabatic cooling resulting from large-scale vertical ascent. Under this fundamental equilibrium, the monthly average large-scale vertical motion (ω) serves as a robust proxy for the integrated heating of the atmospheric column. Therefore, while high-frequency weather features a two-way feedback between latent heat and updrafts, on a monthly timescale, this integrates into a macroscopic thermodynamic equilibrium. Because this balance is achieved within the same month, it manifests statistically as a strong contemporaneous (lag-0) coupling, which our methodology explicitly targets and resolves.
- Empirical verification (PCMCI+ Causal Discovery): To ensure that our index was built upon a robust physical foundation despite these high-frequency feedbacks, we explicitly investigated contemporaneous (lag-0) interactions using the PCMCI+ causal discovery algorithm. As established by Runge (2020), PCMCI+ represents unresolvable contemporaneous interactions or Markov equivalence classes as unoriented links (∘−∘). Consistent with your premise regarding tightly coupled two-way interactions, our initial causal network (excluding the BWR) could not resolve the directionality between mid-tropospheric vertical velocity (ω) and precipitation, resulting in an unoriented link (ω∘−∘Precipitation) as shown in Figure 6a. However, when the BWR is introduced into the network (Figure 6b), the algorithm successfully resolves this ambiguity. It identifies a clear, directed causal hierarchy where ω structurally drives the BWR, which in turn exerts a direct causal influence on precipitation (ω→BWR→Precipitation). This empirical verification confirms that while ω and precipitation are tightly coupled, the BWR successfully extracts the large-scale thermodynamic-dynamic constraints from the unoriented high-frequency feedbacks, proving its robustness as a unidirectional climate-scale predictor.
(3) Author's changes in manuscript: We have expanded Section 5.3 to explicitly acknowledge the high-frequency two-way interaction between latent heat release and upward motion, clarifying how the monthly temporal scale accounts for this dynamic.
Point 2(1) Comment from referee: Since the PCMCI+ causal discovery algorithm is one of the core methodologies of this study, the current description of this method is rather vague, which may hinder the reader’s understanding of the subsequent results, particularly those presented in Fig. 6.
(2) Author's response: We thank you for highlighting this. We agree that a more comprehensive explanation of the PCMCI+ algorithm is necessary, given its central role in isolating the dynamic and thermodynamic drivers of precipitation in our study. We believe these additions provide the necessary context for readers to fully understand the robustness of the causal hierarchy presented in the results.
(3) Author's changes in manuscript: In the revised manuscript, we have significantly expanded the description of the PCMCI+ framework in Section 3.3.1, as well as lines 205-210, to ensure the methodology and the subsequent results in Figure 6 are fully transparent to the reader. Specifically, we have added text clarifying the following key components of the method:
- The Two-Step Framework: We now explicitly describe how PCMCI+ operates. First, it uses a variant of the PC algorithm for condition-selection to identify the relevant parents for each variable, effectively filtering out spurious autocorrelations. Second, it applies the Momentary Conditional Independence (MCI) test to estimate the causal strength (partial correlation) between variables while conditioning on these identified parents.
- Contemporaneous Links (lag-0): We clarified why the "+" in PCMCI+ is critical for our study. By permitting the discovery of contemporaneous (lag-0) causal links, the algorithm can capture rapid atmospheric adjustments—such as the thermodynamic triggering of convection—that occur faster than our monthly sampling resolution.
- Interpretation of Figure 6: We have added a dedicated paragraph to help readers interpret the causal networks. We explicitly define that the arrows indicate causal direction, the node colors/labels represent the MCI partial correlation values (causal strength), and the percentages represent the reliability of these links based on 3000 bootstrap samples.
Point 3(1) Comment from referee: I wonder whether BWR is applicable beyond the NWSA, and whether its performance varies across regions with different dynamical and moisture regimes, such as the tropics, subtropics, and midlatitudes.
(2) Author's response: We sincerely thank you for raising this important point regarding the broader applicability of the Buoyancy Work Rate (BWR) index. We agree that the performance of the BWR will vary significantly across different dynamical and moisture regimes. Because the BWR was specifically engineered for the "dynamically limited" regime of the NWSA, its direct translation to other latitudes requires careful physical consideration.
- Other Tropical Regions: The BWR is highly applicable to other tropical regions characterized by persistent dynamic limitations, such as those dominated by the descending branches of the Walker circulation. However, its direct use in "moisture-limited" regions is not recommended. Since the current formulation lacks an explicit humidity term, applying it to moisture-starved environments with strong dynamic lifting ("dry ascent") will yield false positives, overestimating convective precipitation. Furthermore, as shown in Figure 3, the index exhibits lower correlations over the Amazon basin. This occurs because, in this continental regime, dynamic forcing varies independently from the thermodynamic potential. Deep convection in the Amazon is often capped by convective inhibition (CIN). Indices based solely on dynamic forcing and positive buoyancy, such as the BWR or CAPE, do not explicitly account for the energy required to overcome this convective inhibition, leading to lower correlations in these environments. Finally, over the eastern slopes of the Andes, precipitation is frequently driven by mechanical orographic lifting under conditions of weak large-scale vertical motion (ω). These highly localized mechanical processes are not fully resolved at the spatial resolution of the reanalysis data, which can lead to false negatives in the BWR.
- Subtropics and Midlatitudes: We clarify that the BWR is fundamentally a climate index for tropical convection. The theoretical foundation of the index rests on the thermodynamic energy balance proposed by Cornejo-Garrido and Stone (1977), which assumes that latent heat release is primarily balanced by adiabatic cooling. In the midlatitudes, atmospheric dynamics are predominantly governed by baroclinic instability, frontal lifting, and a strong Coriolis influence. Therefore, applying the BWR directly to midlatitude regimes would likely yield physically inconsistent results, as the energy conversion processes driving precipitation differ substantially from the tropical convective heat engine.
(3) Author's changes in manuscript: We have added a new paragraph to the Section 5.3 to explicitly address the index's applicability beyond the NWSA across other tropical, subtropical, and midlatitude regions.
Point 4(1) Comment from referee: Line 80: ERA5 exhibits strong correlations with both RAIN4PE and PISCO in the coastal region between Peru and Ecuador, whereas the correlations weaken in other regions. What accounts for this spatial discrepancy?
(2) Author's response: We thank you for highlighting this spatial discrepancy. We attribute this spatial discrepancy to the varying physical mechanisms that drive precipitation across the domain, as well as inherent observational and resolution constraints in both the reanalysis and reference datasets. The reasons are two-fold:
- Strong correlation on the coast (Large-Scale Forcing and Gauge Density): Precipitation anomalies in the coastal NWSA region are predominantly driven by large-scale atmospheric and oceanic forcings. Because global reanalysis models like ERA5 (which has a spatial resolution of 0.25°) excel at resolving large-scale synoptic and dynamic boundaries, ERA5 correlates very strongly with observation-based datasets in this region. Furthermore, gridded products like PISCO exhibit their highest spatial reliability precisely in coastal areas where there is a high density of meteorological stations.
- Weak correlation in the Andes and Amazon (Topography, Parameterization, and Observational Uncertainty): Conversely, as we move inland toward the Andes and the Amazon basin, the correlation drops significantly due to both model limitations in ERA5 and interpolation uncertainties in the gridded observational products:
* Topography: ERA5’s spatial resolution (0.25°) is too coarse to adequately represent fine-scale orographic precipitation. Consequently, ERA5 has been shown to significantly overestimate precipitation over the complex terrain of the Andes, occasionally producing unrealistically high precipitation at isolated grid points subjected to local orographic forcing. In contrast, observationally-merged products like PISCO and RAIN4PE incorporate local rain-gauge networks and terrain elevation models to better capture orographic lifting.
* Convection Parameterization: Over the Amazon, precipitation is heavily driven by local moisture recycling and mesoscale convective systems. ERA5 relies on convective parameterizations to simulate this rainfall, which often fail to capture the precise magnitude and timing of localized convective bursts compared to observationally-merged products.
* Observational Uncertainty (Gauge Density): Furthermore, gridded products like PISCO and RAIN4PE are highly dependent on in situ data to correct satellite biases. Because rain gauges are unevenly and sparsely distributed across the Amazon basin, the high accuracy of these products is strictly constrained to well-gauged regions. In regions with severe data voids like the Amazon, the spatial interpolation used to generate these datasets can lead to significant overestimation or underestimation of precipitation, resulting in an inconsistent temporal distribution. Therefore, the weakened correlation in the Amazon is a product of both ERA5 parameterization limits and inherent observational uncertainties in the reference datasets.(3) Author's changes in manuscript: We have expanded the line 80 to explain the reasons that account for this spatial discrepancy in the revised manuscript.
Point 5(1) Comment from referee: Line 170–175: Why do CAPE, BWR, and GDI exhibit strong positive correlations with precipitation along the coastal region, while these relationships weaken or even become negative over the Amazon?
(2) Author's response: We appreciate your careful attention to the spatial correlation maps. This contrast highlights a fundamental difference in the convective regimes between the coastal NWSA and the Amazon basin. The spatial divergence in correlation can be explained by the following physical distinctions, which highlight the specific applicability of the BWR:
- The Coastal Regime (Dynamically Limited): Along the coastal region, precipitation is heavily constrained by the persistent large-scale subsidence of the Walker circulation. When this dynamic suppression relaxes and coincides with local surface warming, the atmospheric column rapidly destabilizes. Consequently, both convective indices and precipitation increase simultaneously, resulting in the strong positive correlations observed.
- The Amazon Regime (Thermodynamically Abundant, Dynamically Independent): In contrast, the Amazon is a continental regime where dynamic forcing varies independently from the abundant thermodynamic potential. In this region, high thermodynamic instability frequently coexists with convective inhibition (CIN). Furthermore, during driest months, the intense solar radiation heats the surface, building up massive amounts of instability. Conversely, during highly rainy months, extensive cloud cover and evaporative cooling lower the surface temperatures, which suppresses these thermodynamic values. This out-of-phase relationship between convective consumption (cloud-shading) and instability build-up on a monthly scale naturally leads to the weak or even negative correlations observed. Indices based solely on dynamic forcing or positive buoyancy, do not explicitly account for the energy required to overcome this CIN, leading to lower correlations in these environments.
(3) Author's changes in manuscript: We have expanded the explanation of the strong correlations in the coastal and the weak correlations over the Amazon in the Line 170-175.
Point 6(1) Comment from referee: Line 85: ‘(81.95° W–67.05° W, 18.95° S–1.95° N)’ instead of ‘(18.95° S–1.95° N, 81.95° W–67.05° W)’.
(2) Author's response: We thank you for catching this formatting detail. We agree completely.
(3) Author's changes in manuscript: We have corrected the coordinate order to follow the standard (Longitude, Latitude) convention in the revised manuscript.
Citation: https://doi.org/10.5194/egusphere-2026-1049-AC1
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AC1: 'Reply on RC1', Jose Obregon-Yataco, 10 Jun 2026
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This study focuses on hydroclimatic extremes over Northwestern South America (NWSA), particularly during El Niño events, and highlights the limitations of thermodynamic indices in explaining precipitation anomalies. To address this, the authors propose a new diagnostic metric, the Buoyancy Work Rate (BWR), which integrates thermodynamic instability and large-scale dynamically forced vertical motion. Using the PCMCI+ causal discovery framework, the study demonstrates that precipitation variability in the region is primarily controlled by large-scale dynamics, with vertical motion exerting a stronger causal influence than local thermodynamic processes. The BWR is further shown to outperform traditional indices in capturing extreme precipitation through tail dependence analysis, while also providing enhanced signal persistence. Overall, the study presents BWR as a physically grounded and potentially more reliable predictor for sub-seasonal hydroclimatic extremes in NWSA. The topic is interesting, and the whole research is logical and well organized. Thus, this paper could be suitable for publication after addressing the following questions.
Comments:
1. Precipitation and ascending motion are closely coupled, each influencing the other in a two-way interaction. In particular, latent heat released during precipitation formation warms the surrounding atmosphere and promotes local upward motion. Conversely, ascending motion creates favorable dynamical conditions for moisture condensation and precipitation development. The authors should clarify whether the interaction between precipitation and upward motion may influence the applicability of BWR over the NWSA.
2. Since the PCMCI+ causal discovery algorithm is one of the core methodologies of this study, the current description of this method is rather vague, which may hinder the reader’s understanding of the subsequent results, particularly those presented in Fig. 6.
3. I wonder whether BWR is applicable beyond the NWSA, and whether its performance varies across regions with different dynamical and moisture regimes, such as the tropics, subtropics, and midlatitudes.
4. Line 80: ERA5 exhibits strong correlations with both RAIN4PE and PISCO in the coastal region between Peru and Ecuador, whereas the correlations weaken in other regions. What accounts for this spatial discrepancy?
5. Line 170–175: Why do CAPE, BWR, and GDI exhibit strong positive correlations with precipitation along the coastal region, while these relationships weaken or even become negative over the Amazon?
6. Line 85: ‘(81.95° W–67.05° W, 18.95° S–1.95° N)’ instead of ‘(18.95° S–1.95° N, 81.95° W–67.05° W)’.