Explaining monthly precipitation anomalies in northwestern South America by integrating vertical dynamics and energetics

Obregon-Yataco, Jose

doi:10.5194/egusphere-2026-1049

Preprints

https://doi.org/10.5194/egusphere-2026-1049

Preprints

25 Mar 2026

| 25 Mar 2026

Explaining monthly precipitation anomalies in northwestern South America by integrating vertical dynamics and energetics

Jose Obregon-Yataco

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 (λ_U) reveals that the BWR achieves robust asymptotic dependence (λ_U ~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.

Received: 24 Feb 2026 – Discussion started: 25 Mar 2026

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Jose Obregon-Yataco

Status: final response (author comments only)

RC1:
'Comment on egusphere-2026-1049', Anonymous Referee #1, 09 Jun 2026

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)’.

Citation: https://doi.org/10.5194/egusphere-2026-1049-RC1
- AC1: 'Reply on RC1', Jose Obregon-Yataco, 10 Jun 2026
  
  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
RC2: 'Comment on egusphere-2026-1049', Anonymous Referee #2, 15 Jun 2026

The current manuscript by Obregon-Yataco introduces an interesting index for diagnosing conditions associated with precipitation anomalies at the monthly time scale. This BWR index includes the relationship between vertical velocity and buoyancy, via the product omega*deltaT, based on the deltaT from by parcel theory. The author finds that, compared with other indices, the BWR index exhibits a larger correspondence with precipitation anomalies at the montly time scale over parts of Peru and neighboring regions. In addition, the author provides diagnostics that show the stronger role of dynamic forcing vs. local surface fluxes on precipitation anomalies, which provides support to the use of the BWR index.

The manuscript is clear and it provides interesting results, including the diagnostic potential of the BWR index. However, there is room for improvement and clarification. Below I include some comments that hopefully can contribute to reaching a more complete and robust version of the current study.
General comments:

-----------------
1. In general, the BWR already contains the development of convection, via the ascending motion quantified with omega. This fact alone could explain the larger consistency (via correlations, PCMI and other indices) between BWR and precipitation, compared to other indices like CAPE, GDI, etc. In this sense, the BWR is an interesting proxy diagnostic (as the author clearly states it), that could be useful for simplified monitoring and diagnosis, e.g. for using in a similar way as a stream-function (not similar in mathematical nature, though).

From a physical point of view, the relationship between omega (and therefore BWR) and precipitation is more direct, since ascending motion is already an atmospheric response to more fundamental drivers, like convective instability and/or horizontal convergence. In this sense, the BWR index would not be on the same grounds as CAPE or GDI. While the latter attempt to quantify the potential for convection and precipitation (via precursor conditions), the BWR index already includes a measure of the atmospheric response (not potential), via omega.

Taking into account these considerations, some parts of the current text could be misleading, suggesting that BWR has predictive power, when physically it already contains the response, not only the drivers. I suggest to the author to make more clear the relationship between omega and the atmospheric response, e.g. with ascent already being part of the atmospheric response, similar to precipitation.
2. The author says that the BWR could also be useful for early warning, which is associated with prediction. Maybe, filtering the smaller horizontal scales in omega (to make sure that only the larger scale environment is left) before computing BWR, could lead to a more transparent formulation of an index that attempts to measure precursor conditions leading eventualy to precipitation anomalies. In the case of prediction, a filtered version of BWR could be an indicator of large-scale conditions favorable (or unfavorable) for precipitation anomalies. However, the BWR index in its current form is purely diagnostic. In this sense, one could think that predicted precipitation anomalies from models could be as useful as the BWR index from predicted fields. I suggest the author to clarify those parts of the text where he refers to the predictability capabilities of the BWR index.
3. The PCMCI+ algorithm is used first to verify the hypothesis that: "the large scale dynamics [omega] exert a stronger control on precipitation than local surface fluxes [evaporation]". However, this analysis is not novel. Studies as old as the one by Cornejo-Garrido and Stone already demonstrated this type of result. In fact, in their study, they emphasize on the role of horizontal convergence. In general, the tremendous importance of horizontal convergence (at low- and/or mid-levels), moisture transport from remote sources, and anomalies in regional circulation structures (e.g. the regional branch of the Walker circulation), has been documented in many papers. I suggest the author to review such literature in orther to update or to provide a different focus to the component associated with surface vs. dynamic drivers.
Specific comments:

-----------------
L42-43: Please describe briefly what these indices are.

L81: "being more strong" -> "being stronger"

L85-86: A figure with the domains should be included in the main text, in order to facilitate the reading.

L94: "window where dynamic" -> "window when dynamic"

L100-105: please provide a brief justification for the selection of the thresholds, e.g. do they correspond to special percentiles? or are they associated with specific impacts or relevant events (Fig. 7)? These thresholds should not be so "arbitrary".

L106-109: It would be interesting to see some figures about this, e.g. as supplementary material.

L113-L114: The author says that, for precipitation, vertical velocity is its trigger, and buoyancy is its fuel. This statement could be misleading. Instead, buoyancy can lead to vertical flow, i.e. instability is a trigger for convection.

L125-128. It would be instructive to briefly compare the definitions of BWR and CAPE.

L151-152. The author refers to El Niño-related precipitation anomalies as "extreme precipitation". In order to distinguish from "meteorological extreme precipitation" (hours-days), it would be more clear to use the term "climate extremes", or "extreme hydroclimatic anomalies" (L233) instead.

L182-185. The RMSE is commonly used for two quantities representing the same variable, because in this case it provides a clear measure of the distance or "error" of one variable with respect to the other (one of them being considered as a reference or ground truth). However, in the case of different variables (e.g. BWR vs. precipitation) it is easier to interpret the correlation coefficient than the RMSE obtained from the standarized anomalies. The latter compare non-dimensional variables, which convey information about the timing and relative sizes of fluctuations (information already available in the correlation coefficient), but not about the magnitudes of the original variables (which in the case of BWR vs. precipitation are not comparable in magnitude). In this sense, talking about "bias correction" when comparing standired anomalies is not so informative.

L190: This line seems incomplete.

L195-198: BWR, CAPE and ERA5 precipitation are derived from the ERA5 reanalysis. This explains why they are consistent among them. It would be better to compare to other precipitation estimates, like from the GPM-IMERG dataset, in order to better support the comments about the PISCO data set.

L200-232: In order to have a more direct comparison, it would be convenient to have a version of Fig. 6a with "physical link assumptions", so that a more direct comparison with Fig. 6b could be attempted. In addition, some variables could be modified before constructing Fig. 6, to facilitate the interpretation of the MCI values, e.g. having evaporation positive when directed towards the atmosphere (line 209), and vertical velocity positive when upwards.

L244. The author says that positive precipitation anomalies stimulated deep convection. But physically, it is the other way around. Please clarify.

L242-269 : Section 4.3.1 provides a context, mostly supported on previous studies. This section is not needed in the main text. Instead, the author can make a very brief reference (e.g. 2 or 3 lines) to the cited studies in order to pinpoint specific years, or move this subsection to the supplementary material.

L270-283: Section 4.3.2. This section is not very deep, and in its current form does not provide additional insight. It would be useful to diagnose horizontal mid-level convergence, as apparent for years 1998 and 2017, for example.

L285. Figure 11. The legends in the figures should include the name of the variable. I guess that the units were included in order to use a single horizontal numerical axis: this should be explained in the caption. In addition, the horizontal lines for the LCL, LFC and EL advertised in the caption are not included in the figures.

L283-299: Section 4.3.3. In this section the author can make a more detailed analysis of the vertical levels on which each variable (omega, delta-T, omega*delta-T) exhibit more interesting features. For example: what are the typical vertical levels at which omega*delta-T is the largest?

L300-319: Section 4.3.4. This section shows the diagnostic nature of the BWR index (line 313). The BWR already contains the atmospheric response to regional circulation drivers (e.g. regional anomalies in the Walker circulation), via omega. The the atmospheric response could also be assessed in terms of precipitation anomalies directly. Please expand on how the BWR provides information that is additional to the precipitation anomalies, e.g. for the 2016 event.

L354. The author talks about "predictive memory", but this sounds contradictory. Maybe a better term would be "predictive capability".

Citation: https://doi.org/10.5194/egusphere-2026-1049-RC2

Jose Obregon-Yataco

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Short summary

Standard weather indices often fail to predict rainfall extremes in northwestern South America during El Niño events. To fix this, we developed the Buoyancy Work Rate, a new indicator combining heat energy with vertical air movement. Our analysis proves this method filters out false alarms, explaining why some warm years are dry while others cause massive floods. This provides a more reliable tool for early warning systems and disaster risk reduction in vulnerable coastal regions.


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