Exploratory Precipitation Metrics: Spatiotemporal Characteristics, Process-Oriented, and Phenomena-Based

Precipitation sustains life and supports human activities, making its prediction one of the most societally relevant challenges in weather and climate modeling. Limitations in modeling precipitation underscore the need for diagnostics and metrics to evaluate precipitation in simulations and predictions. While routine use of basic metrics is important for documenting model skill, more sophisticated diagnostics and metrics aimed at connecting model biases to their sources and revealing precipitation characteristics relevant to how model precipitation is used are critical for improving models and their uses. This paper illustrates examples of exploratory diagnostics and metrics including 1) spatiotemporal characteristics metrics such as diurnal variability, probability of extremes, duration of dry spells, spectral characteristics, and spatiotemporal coherence of precipitation; 2) process-oriented metrics based on the rainfall–moisture coupling and temperature–water vapor environments of precipitation; and 3) phenomena-based metrics focusing on precipitation associated with weather phenomena including low pressure systems, mesoscale convective systems, frontal systems, and atmospheric rivers. Together, these diagnostics and metrics delineate the multifaceted and multiscale nature of precipitation, its relations with the environments, and its generation mechanisms. The metrics are applied to historical simulations from phases 5 and 6 of the Coupled Model Intercomparison Project. Models exhibit diverse skill as measured by the suite of metrics, with very few models consistently ranked as top or bottom performers compared to other models in multiple metrics. Analysis of model skill across metrics and models suggests possible relationships among subsets of metrics, motivating the need for more systematic analysis to understand model biases for informing model development.

Leung, L. R., Boos, W. R., Catto, J. L., A. DeMott, C., Martin, G. M., Neelin, J. D., O’Brien, T. A., Xie, S., Feng, Z., Klingaman, N. P., Kuo, Y., Lee, R. W., Martinez-Villalobos, C., Vishnu, S., Priestley, M. D. K., Tao, C., & Zhou, Y. (2022). Exploratory Precipitation Metrics: Spatiotemporal Characteristics, Process-Oriented, and Phenomena-Based, Journal of Climate35(12), 3659-3686

Figure 2. Observational (GPCP and TRMM-3B42) and selected models: (a) daily precipitation PDFs in the eastern United States (25°–48°N, 257°–294°E) and (b) dry spell durations PDFs in the western United States (30°–48°N, 236°–257°E). In (a) and (b) the cutoff scales are shown by a large circle (for models) or large squares (for observational datasets). Note that the larger or longer the cutoff scale, the more extreme is the large event tail. (c). Multimodel mean (out of 35 models) of the daily precipitation cutoff-scale PL pattern. (d). Multimodel mean of the dry spell duration cutoff-scale tL pattern (with model-dependent dry-day precipitation threshold). (e). Scatterplot of the PL scaling factor and pattern correlation coefficient against TRMM-3B42 for individual models [numbers; legend across (e) and (f) gives corresponding acronyms], multimodel mean (green dot), GPCP (orange dot), and TRMM-3B42 [blue dot at (1, 1) by definition. (f). As in (e), but for tL scaling factor and pattern correlation coefficient.

Revealing the Circulation Pattern Most Conducive to Precipitation Extremes in Henan Province of North China

Two catastrophic extreme precipitation events in July 2021 and August 1975 caused tremendous
damages and deaths in Henan, one of the most populated provinces in China. Revealing the relationship
between large-scale circulation patterns and precipitation extremes is vital for understanding the physical mechanisms and providing potential value for improving prediction and hence reducing impacts. Here, nine large-scale circulation patterns are identified for July–August using the self-organizing map. We find daily precipitation extremes under the fifth pattern (P5), characterized with the strongest easterly wind anomalies in Henan, feature the highest frequency and the largest intensity. Seven out of total 11 days in the two catastrophic extreme precipitation events belong to P5, and the top two maximum hourly precipitation extremes over continental China occurred under P5. The larger intensity of precipitation extremes is attributed to the dynamical contribution, suggesting more-intense precipitation extremes under P5 are largely dominated by stronger ascending motions.

Zhang, S., Y. Chen, Y. Luo, B. Liu, G. Ren, T. Zhou, C. Martinez-Villalobos, and M. Chang, (2022): Revealing the circulation pattern most conducive to precipitation extremes in Henan Province of North China. Geophysical Research Letters, 49, e2022GL098034. https://doi.org/10.1029/2022GL098034

Figure 2. The composite daily anomalies of geopotential height (colored shading, unit: gpm) at 500 hPa and column-integrated moisture flux (arrows; units: kg·m−1·s−1) in the 3 × 3 self-organizing map (SOM) nodes. Green lines denote 5,860 and 5,880 gpm contours. The number and occurrence frequency for each pattern are indicated in the upper-right corner. In the lower-left corner, ρ1 represents the mean pattern correlations for 500 hPa geopotential height between the composite pattern and each pattern in the corresponding SOM node, while ρ2 is calculated as the average of the two mean pattern correlations for zonal and meridional column integrated moisture fluxes, respectively

Precipitation extremes and water vapor: Relationships in current climate and implications for climate change

Purpose of Review:

Review our current understanding of how precipitation is related to its thermodynamic environment, i.e., the water vapor and temperature in the surroundings, and implications for changes in extremes in a warmer climate.

Recent Findings:

Multiple research threads have i) sought empirical relationships that govern onset of strong convective precipitation, or that might identify how precipitation extremes scale with changes in temperature; ii) examined how such extremes change with water vapor in global and regional climate models under warming scenarios; iii) identified fundamental processes that set the characteristic shapes of precipitation distributions.


While water vapor increases tend to be governed by the Clausius-Clapeyron relationship to temperature, precipitation extreme changes are more complex and can increase more rapidly, particularly in the tropics. Progress may be aided by bringing separate research threads together and by casting theory in terms of a full explanation of the precipitation probability distribution.

Neelin, J.D., Martinez-Villalobos, C., Stechmann, S.N. et al. Precipitation Extremes and Water Vapor. Curr Clim Change Rep 8, 17–33 (2022). https://doi.org/10.1007/s40641-021-00177-z

Figure 5. Examples of changes in key aspects of precipitation pdfs under warming. a US Northeast daily precipitation pdfs in CESM2 simulated for historical (blue; 1990–2014) and end-of-century (red; 2075 2099) SSP5-8.5 scenario radiative forcing. Note increases in the extreme tail under global warming associated with an increase in the precipitation scale PL. b Daily precipitation risk ratios in two different regions (indicated by red boxes in c) for CESM2. Systematic increases for the largest events are controlled by Delta PL versus PL. c Percent change in PL between 2075–2099 compared to 1990–2014 in CESM2. d Same as a but for GFDL-CM4. The 7% K−1 contour interval corresponds approximately to multiples of CC scaling.

Understanding future increases in precipitation extremes in global land monsoon regions

This study investigates future changes in daily precipitation extremes and the involved physics over the global land monsoon (GM) region using climate models from phase 6 of the Coupled Model Intercomparison Project (CMIP6). The daily precipitation extreme is identified by the cutoff scale, measuring the extreme tail of the precipitation distribution. Compared to the historical period, multimodel results reveal a continuous increase in precipitation extremes under four scenarios, with a progressively higher fraction of precipitation exceeding the historical cutoff scale when moving into the future. The rise of the cutoff scale by the end of the century is reduced by 57.8% in the moderate emission scenario relative to the highest scenario, underscoring the social benefit in reducing emissions. The cutoff scale sensitivity, defined by the increasing rates of the cutoff scale over the GM region to the global mean surface temperature increase, is nearly independent of the projected periods and emission scenarios, roughly 8.0% K−1 by averaging all periods and scenarios. To understand the cause of the changes, we applied a physical scaling diagnostic to decompose them into thermodynamic and dynamic contributions. We find that thermodynamics and dynamics have comparable contributions to the intensified precipitation extremes in the GM region. Changes in thermodynamic scaling contribute to a spatially uniform increase pattern, while changes in dynamic scaling dominate the regional differences in the increased precipitation extremes. Furthermore, the large intermodel spread of the projection is primarily attributed to variations of dynamic scaling among models.

Chang M., B. Liu, B. Wang, C. Martinez-Villalobos, G. Ren, and T. Zhou, 2022: Understanding future increases in precipitation extremes in global land monsoon regionsJ. Climate, 35(6)1839-1851https://doi.org/10.1175/JCLI-D-21-0409.1

Figure 7. Multi-model mean (a) precipitation extremes and (b) full scaling of extreme precipitation derived using (4) for all days with daily precipitation exceeding PM in 1995-2014. Multi-model mean of fractional changes relative to the period 1995-2014 of (c) precipitation extremes and (d) full scaling for all days with daily precipitation exceeding PM in the long-term under SSP2-4.5 scenario. The red lines denote the boundaries of global land monsoon region.

Climate models capture key features of extreme precipitation probabilities across regions (February 2021)

Quantitative simulation of precipitation in current climate has been an ongoing challenge for global climate models. Despite serious biases in correctly simulating probabilities of extreme rainfall events, model simulations under global warming scenarios are routinely used to provide estimates of future changes in these probabilities. To minimize the impact of model biases, past literature tends to evaluate fractional (instead of absolute) changes in probabilities of precipitation extremes under the assumption that fractional changes would be more reliable. However, formal tests for the validity of this assumption have been lacking. Here we evaluate two measures that address properties important to the correct simulation of future fractional probability changes of precipitation extremes, and that can be assessed with current climate data. The first measure tests climate model performance in simulating the characteristic shape of the probability of occurrence of daily precipitation extremes and the second measure tests whether the key parameter governing the scaling of this shape is well reproduced across regions and seasons in current climate. Contrary to concerns regarding the reliability of global models for extreme precipitation assessment, our results show most models lying within the current range of observational uncertainty in these measures. Thus, most models in the Coupled Model Intercomparison Project Phase 6 ensemble pass two key tests in current climate that support the usefulness of fractional measures to evaluate future changes in the probability of precipitation extremes.

Cristian Martinez-Villalobos and J David Neelin 2021 Environ. Res. Lett. 16 024017, https://doi.org/10.1088/1748-9326/abd351

Figure 1. (a) Probability distributions for the region shown in figure 2(a) calculated from four observational datasets (GPCP, PERSIANN V1, CMORPH v1 and TRMM-3B42; squares) and one CMIP6 model (GFDL-CM4, black circles). Note the different cutoff scales PL in each dataset (big circle markers). (b) As in (a) but rescaled by their respective PL , allowing similarities in the shape of the extreme tail (above $P^{*} = \frac{P}{P_{L}} = 1$) to be evaluated. Big circle markers shows the location of the cutoff-scale in P coordinates ($P_{L}^{*} = 1$ in all cases). In addition to datasets in (a), rescaled distributions in ACCESS-ESM1-5, CanESM5, CESM2, FGOALS-g3, INM-CM5-0 and IPSL-CM6A-LR are also shown. (c) Schematic of the effect of an increase in the cutoff scale $P_{L}^{*}$ on the extreme tail probability. This is illustrated in rescaled coordinates but same fractional changes apply for daily precipitation before rescaling. As an example, we use a fractional increase in $P_{L}^{*}$ of 21%, which (under no changes in dynamical contribution) would correspond to a Clausius–Clapeyron scaling for a 3 °C temperature increase. Using same τP  = 0.5 for both curves yields a fractional increase of the 99.9th daily precipitation percentile $P_{99.9}^{*}$ (over wet days) also of 21%. The actual fractional increase of $P_{99.9}^{*}$ (or P99.9) will have a small dependence on how τP adjusts (see supplementary material).

Changes in Extreme Precipitation Accumulations during the Warm Season over Continental China (December 2020)

Precipitation accumulations, integrated over rainfall events, are investigated using hourly data across continental China during the warm season (May–October) from 1980 to 2015. Physically, the probability of precipitation accumulations drops slowly with event size up to an approximately exponential cutoff scale sL where probability drops much faster. Hence sL can be used as an indicator of high accumulation percentiles (i.e., extreme precipitation accumulations). Overall, the climatology of sL over continental China is about 54 mm. In terms of cutoff changes, the current warming stage (1980–2015) is divided into two periods, 1980–97 and 1998–2015. We find that the cutoff in 1998–2015 increases about 5.6% compared with that of 1980–97, with an average station increase of 4.7%. Regionally, sL increases are observed over East China (10.9% ± 1.5%), Northwest China (9.7% ± 2.5%), South China (9.4% ± 1.4%), southern Southwest China (5.6% ± 1.2%), and Central China (5.3% ± 1.0%), with decreases over North China (−10.3% ± 1.3%), Northeast China (−4.9% ± 1.5%), and northern Southwest China (−3.9% ± 1.8%). The conditional risk ratios for five subregions with increased cutoff sL are all greater than 1.0, indicating an increased risk of large precipitation accumulations in the most recent period. For high precipitation accumulations larger than the 99th percentile of accumulation s99, the risk of extreme precipitation over these regions can increase above 20% except for South China. These increases of extreme accumulations can be largely explained by the extended duration of extreme accumulation events, especially for “extremely extreme” precipitation greater than s99.

Chang, M., B. Liu, C. Martinez-Villalobos, G. Ren, S. Li, and T. Zhou, 2020: Changes in Extreme Precipitation Accumulations during the Warm Season over Continental China. J. Climate33, 10799–10811, https://doi.org/10.1175/JCLI-D-20-0616.1

Fig. 6 (a) Percentage change of sM at each station and (b) mean percentage change of sM for each climate division between 1998–2015 and 1980–97 (1998–2015 minus 1980–97). (c) Percentage changes of sM and PM for eight climate divisions between 1980–97 and 1998–2015. The results in (b) and (c) are based on 1000 bootstrap (with replacement) realizations, and the boxes in (c) represent the 50th percentile with the error bars represent the 5th–95th percentiles. The color box of the legend in (a) represents the range within the adjacent two labels while the color box of the legend in (b) represents the label at the center of the color box.

Why Do Precipitation Intensities Tend to Follow Gamma Distributions? (published November 2019)

The probability distribution of daily precipitation intensities, especially the probability of extremes, impacts a wide range of applications. In most regions this distribution decays slowly with size at first, approximately as a power law with an exponent between 0 and −1, and then more sharply, for values larger than a characteristic cutoff scale. This cutoff is important because it limits the probability of extreme daily precipitation occurrences in current climate. There is a long history of representing daily precipitation using a gamma distribution—here we present theory for how daily precipitation distributions get their shape. Processes shaping daily precipitation distributions can be separated into nonprecipitating and precipitating regime effects, the former partially controlling how many times in a day it rains, and the latter set by single-storm accumulations. Using previously developed theory for precipitation accumulation distributions—which follow a sharper power-law range (exponent < −1) with a physically derived cutoff for large sizes—analytical expressions for daily precipitation distribution power-law exponent and cutoff are calculated as a function of key physical parameters. Precipitating and nonprecipitating regime processes both contribute to reducing the power-law range exponent for the daily precipitation distribution relative to the fundamental exponent set by accumulations. The daily precipitation distribution cutoff is set by the precipitating regime and scales with moisture availability, with important consequences for future distribution shifts under global warming. Similar results extend to different averaging periods, providing insight into how the precipitation intensity distribution evolves as a function of both underlying physical climate conditions and averaging time.

Martinez-Villalobos, C. and J.D. Neelin2019Why Do Precipitation Intensities Tend to Follow Gamma Distributions?. J. Atmos. Sci., 763611–3631, https://doi.org/10.1175/JAS-D-18-0343.1






Fig. 2. Accumulations (blue circles) and daily precipitation (red circles) distributions in (a) observations at Manus Island (2°S, 147°E; January 1998, September 2012), (b) generated by the model with on–off precipitation, and (c) generated by the model with ramp precipitation. Parameters of the models are E = 0.1 mm h−1C¯=0.2 mm h−1b = 0.2 mm, DE = 3 mm h−1/2qc = 65 mm, with R0 = 9 mm h−1 and DP = 17 mm h−1/2 in the model with on–off precipitation, and α = 0.35 h−1 and DP = 12 mm h−1/2 in the model with ramp precipitation. Parameters are selected to generate similar accumulation and duration moment ratios (⟨s2⟩/⟨s⟩ and ⟨t2⟩/⟨t⟩, respectively, with ⟨⋅⟩ denoting the expectation value) compared to Manus Island observations. All model parameters are also listed in Table S1. Accumulation and daily precipitation distributions are fitted following appendix A (blue and red solid lines, respectively) only taken into account bins with 10 or more counts, except for accumulations in the on–off precipitation case, where the analytical formula (9) is used. Blue and red dashed lines show only the power-law part of the fits to the accumulation and daily precipitation distributions.

Observed El Niño-La Niña Asymmetry in a Linear Model (published August 2019)

Previous studies indicate an asymmetry in the amplitude and persistence of El Niño (EN) and La Niña (LN) events. We show that this observed EN‐LN asymmetry can be captured with a linear model driven by correlated additive and multiplicative (CAM) noise, without resorting to a deterministic nonlinear model. The model is derived from 1‐month lag statistics taken from monthly sea surface temperature (SST) data sets spanning the twentieth century, in an extension of an empirical‐dynamical technique called Linear Inverse Modeling. Our results suggest that noise amplitudes tend to be stronger for EN compared to LN events, which is sufficient to generate asymmetry in amplitude and also produces more persistent LN events on average. These results establish a null hypothesis for EN‐LN asymmetry and suggest that strong EN events may not be more predictable that what can be accounted for by a multivariate linear system driven by CAM noise.

C., Martinez‐Villalobos, Newman, M., Vimont, D. J., Penland, C., & Neelin, J. D. ( 2019). Observed El Niño‐La Niña asymmetry in a linear model. Geophysical Research Letters, 46, 9909-9919. https://doi.org/10.1029/2019GL082922



The Role of Stochastic Forcing in Generating ENSO Diversity (published November 2018)

Numerous oceanic and atmospheric phenomena influence El Niño–Southern Oscillation (ENSO) variability, complicating both prediction and analysis of the mechanisms responsible for generating ENSO diversity. Predictability of ENSO events depends on the characteristics of both the forecast initial conditions and the stochastic forcing that occurs subsequent to forecast initialization. Within a linear inverse model framework, stochastic forcing reduces ENSO predictability when it excites unpredictable growth or interference after the forecast is initialized, but also enhances ENSO predictability when it excites optimal initial conditions that maximize deterministic ENSO growth. Linear inverse modeling (LIM) allows for straightforward separation between predictable signal and unpredictable noise and so can diagnose its own skill. While previous LIM studies of ENSO focused on deterministic dynamics, here we explore how noise forcing influences ENSO diversity and predictability. This study identifies stochastic forcing details potentially contributing to the development of central Pacific (CP) or eastern Pacific (EP) ENSO characteristics. The technique is then used to diagnose the relative roles of initial conditions and noise forcing throughout the evolution of several ENSO events. LIM results show varying roles of noise forcing for any given event, highlighting its utility in separating deterministic from noise-forced contributions to the evolution of individual ENSO events. For example, the strong 1982 event was considerably more influenced by noise forcing late in its evolution than the strong 1997 event, which was more predictable with long lead times due to its deterministic growth. Furthermore, the 2014 deterministic trajectory suggests that a strong event in 2014 was unlikely.

Thomas, E.E., D.J. Vimont, M. Newman, C. Penland, and C. Martínez-Villalobos, 2018: The Role of Stochastic Forcing in Generating ENSO Diversity. J. Climate, 31, 9125–9150, https://doi.org/10.1175/JCLI-D-17-0582.1



Shifts in Precipitation Accumulation Extremes During the Warm Season Over the United States (published August 2018)

Precipitation accumulations, integrated over precipitation events in hourly data, are examined from 1979 to 2013 over the contiguous United States during the warm season (May–October). As expected from theory, accumulation distributions have a characteristic shape, with an approximate power law decrease with event size followed by an exponential drop at a characteristic cutoff scale sL for each location. This cutoff is a predictor of the highest accumulation percentiles and of a similarly defined daily precipitation cutoff PL. Comparing 1997–2013 and 1979–1995 periods, there are significant regional increases in sL in several regions. This yields distribution changes that are weighted disproportionately toward extreme accumulations. In the Northeast, for example, risk ratio (conditioned on occurrence) for accumulations larger than 109 mm increases by a factor of 2–4 (5th–95th). These changes in risk ratio as a function of size, and connection to underlying theory, have counterparts in the observed daily precipitation trends.

Martinez‐Villalobos, C., & Neelin, J. D. (2018). Shifts in precipitation accumulation extremes during the warm season over the United States. Geophysical Research Letters, 45, 8586–8595. https://doi.org/10.1029/2018GL078465