A Spatiotemporal Stochastic Model for Tropical Precipitation and Water Vapor Dynamics

Self Cite

Clouds are repeatedly identified as a leading source of uncertainty in future climate predictions. Of particular importance are stratocumulus clouds, which can appear as either (i) closed cells that reflect solar radiation back to space or (ii) open cells that allow solar radiation to reach the Earth's surface. Here we show that these clouds regimes—open versus closed cells—fit the paradigm of a phase transition. In addition, this paradigm characterizes pockets of open cells as the interface between the open‐ and closed‐cell regimes, and it identifies shallow cumulus clouds as a regime of higher variability. This behavior can be understood using an idealized model for the dynamics of atmospheric water as a stochastic diffusion process. With this new conceptual viewpoint, ideas from statistical mechanics could potentially be used for understanding uncertainties related to clouds in the climate system and climate predictions.

“…The value of

\overset{σ}{true}

is defined as the expected value of σ ( x , y , t ), in the stationary state, and it can be calculated analytically (see supporting information) as

\overset{σ}{true} = \frac{1}{2} ([], 1 + erf ((), \frac{τF}{\sqrt{2 Var (q_{ij})}})) \approx \frac{1}{2} ([], 1 + erf ((), \frac{τF}{D} \sqrt{\frac{2 πb}{\log (L / Δx)}})),

Var (q_{ij}) \sim D^{2} {(4 πb)}^{- 1} \log (L / Δx)

(see supporting information for derivation assuming Δ x is small). Moreover,

\overset{σ}{true}

depends on

\sqrt{b}

and τ in the same way that it depends on F .…”

Section: Cloud Regimes As Phase Transitionssupporting

confidence: 77%

Section: Idealized Stochastic Model Of Cloudy Boundary Layer Dynamicsmentioning

confidence: 99%

Section: Idealized Stochastic Model Of Cloudy Boundary Layer Dynamicsmentioning

confidence: 99%

“…A cloud indicator variable σ ( x , y , t ) is defined based on whether or not q ( x , y , t ) is above the saturation threshold q = 0 [ Hottovy and Stechmann , ]:

σ (x, y, t) = ({, \begin{matrix} 1 & if & q (x, y, t) \geq 0, \\ 0 & if & q (x, y, t) < 0 . \end{matrix})

…”

Section: Idealized Stochastic Model Of Cloudy Boundary Layer Dynamicsmentioning

confidence: 99%

Section: Cloud Regimes As Phase Transitionsmentioning

confidence: 99%

See 3 more Smart Citations

Cloud regimes as phase transitions

Stechmann

Hottovy

2016

Self Cite

Long temporal autocorrelations in tropical precipitation data and spike train prototypes

Abbott

Stechmann

Neelin

2016

Self Cite

Temporal precipitation autocorrelations drop slower than exponentially at long lags, and there is a range from tens to thousands of minutes where it is relevant to ask if a scale‐free process might underlie the long autocorrelations. A simple stochastic model in which precipitation appears as variable‐length spikes provides a reasonable prototype for this behavior. In both observations and the model, separating the component of the autocorrelation within wet events from the interevent contribution suggests long autocorrelation behavior is primarily associated with the latter. When precipitation spikes are short compared to dry events, a true power law is obtained with analytical exponent −0.5 and precipitation autocorrelation is determined by dry‐spell model parameters. In more realistic cases, wet‐spell termination is also important. Although a variety of apparent power law exponents can be obtained for different parameters, the fundamental long‐lag process appears to be that of the interevent correlation.

Geographical differences in the tropical precipitation‐moisture relationship and rain intensity onset

Ahmed

Schumacher

2017

In this study, we show that the well‐documented exponential increase in the precipitation‐water vapor (P‐r) curve over tropical oceans also applies to tropical land but that the land curve starts its exponential increase at smaller values of column moisture than over ocean. We demonstrate that daytime surface heating contributes to this characteristic shape of the land P‐r curves. There is also significant geographical variation in the shape of the P‐r curve within land and ocean regions, with the Amazon, the Maritime Continent, and the eastern edges of oceans as distinct outliers. We further show that convective and stratiform rain intensities exhibit a pickup that is separate from the corresponding rain areas in the tropical P‐r curve while shallow convective rain has a yet another pickup. These variations of the P‐r curve characteristics likely represent geographical variations of environmental controls on storm life cycle.