Obtaining the drop size distribution

his document is a supplement to “Fluctuations and Luck in Droplet Growth by Coalescence,” by Alexander B. Kostinski and RaymondA. Shaw (Bull. Amer. Meteor. Soc.,86, 235–244) • ©2005 American Meteorological Societ

Spatial patterns of record-setting temperatures

We employ record-breaking statistics to study spatial correlations of record-setting terrestrial surface temperatures. To that end, a simple diagnostic tool is devised, reminiscent of a pair-correlation function. Data analysis reveals that while during the hottest years, record-breaking temperatures arrive in “heat waves”, extending throughout almost the entire continental United States, this is not so for all years, not even recently. Record-breaking temperatures generally exhibit spatial patterns and variability quite different from those of the mean temperatures

Fluctuations and luck in droplet growth by coalescence

After the initial rapid growth by condensation, further growth of a cloud droplet is punctuated by coalescence events. Such a growth process is essentially stochastic. Yet, computational approaches to this problem dominate and transparent quantitative theory remains elusive. The stochastic coalescence problem is revisited and it is shown, via simple back-of-the-envelope results, that regardless of the initial size, the fastest one-in-a-million droplets, required for warm rain initiation, grow about 10 times faster than the average droplet. While approximate, the development presented herein is based on a realistic expression for the rate of coalescence. The results place a lower bound on the relative velocity of neighboring droplets, necessary for warm rain initiation. Such velocity differences may arise from a variety of physical mechanisms. As an example, turbulent shear is considered and it is argued that even in the most pessimistic case of a cloud composed of single-sized droplets, rain can still form in 30 min under realistic conditions. More importantly, this conclusion is reached without having to appeal to giant nuclei or droplet clustering, only occasional “fast eddies.” This is so because, combined with the factor of 10 accelerated growth of the one-in-a-million fastest droplets, the traditional turbulent energy cascade provides sufficient microshear at interdroplet scales to initiate warm rain in cumulus clouds within the observed times of about 30 min. The simple arguments presented here are readily generalized for a variety of time scales, drizzle production, and other coagulation processes

Evolution and distribution of record-breaking high and low monthly mean temperatures

The ratio of record highs to record lows is examined with respect to extent of time series for monthly mean temperatures within the continental United States for 1900–2006. In counting the number of records that occur in a single year, the authors find a ratio greater than unity in 2006, increasing nearly monotonically as the time series increases in length via a variable first year over 1900–76. For example, in 2006, the ratio of record highs to record lows ≈ 13:1 with 1950 as the first year and ≈ 25:1 with 1900 as the first year; both ratios are an order of magnitude greater than 3σ for stationary simulations. This indicates a warming trend. It is also found that records are more sensitive to trends in time series of monthly averages than in time series of corresponding daily values. When the last year (1920–2006, starting in 1900) is varied, it is found that the ratio of record highs to record lows is strongly correlated with the ensemble mean temperature. Correlation coefficients are 0.76 and 0.82 for 1900–2006 and 1950–2006, respectively; 3σ = 0.3 for pairs of uncorrelated stationary time series. Similar values are found for globally distributed time series: 0.87 and 0.92 for 1900–2006 and 1950–2006, respectively. The ratios evolve differently, however: global ratios increase throughout (1920–2006) whereas continental U.S. ratios decrease from about 1940 to 1970. Last, the geographical and seasonal distributions of trends are considered by summing records over time rather than ensemble. In the continental United States, the greatest excess of record highs occurs in February (≈2:1) and the greatest excess of record lows occurs in October (≈2:3). In addition, ratios are pronounced in certain regions: in February in the Midwest the ratio ≈ 5:2, and in October in the Southeast the ratio ≈ 1:2

Terrestrial glint seen from deep space: Oriented ice crystals detected from the Lagrangian point

The Deep Space Climate Observatory (DSCOVR) spacecraft resides at the first Lagrangian point about one million miles from Earth. A polychromatic imaging camera onboard delivers nearly hourly observations of the entire sunlit face of the Earth. Many images contain unexpected bright flashes of light over both ocean and land. We construct a yearlong time series of flash latitudes, scattering angles, and oxygen absorption to demonstrate conclusively that the flashes over land are specular reflections off tiny ice platelets floating in the air nearly horizontally. Such deep space detection of tropospheric ice can be used to constrain the likelihood of oriented crystals and their contribution to Earth albedo. These glint observations also support proposals for detecting starlight glints off faint companions in our search for habitable exoplanets

Entropic aspects of supercooled droplet freezing

The freezing of supercooled water droplets in the atmosphere, with an emphasis on the entropic aspects of the problem, is examined. Supercooled water is a metastable state and, therefore, the associated phase transition must be irreversible. Temperature-dependent heat capacities of supercooled water and ice are used to calculate the entropy difference. That difference is then used to establish a lower bound on the amount of latent heat that can be liberated by the freezing droplets. The calculation is compared with tabulated values of the latent heat of fusion with surprising results. Based on a novel physical picture of the freezing process, the authors suggest a simple estimate for the effective latent heat that is suitable for heat budget calculations of glaciating clouds. In addition, the authors arrive at a quadratic dependence on supercooling, (ΔT)2, for the irreversible contribution to heat exchange during the freezing process. The proportionality factor is estimated as −0.3 J mol−1 K−2

Operational Detection of Sun Glints in DSCOVR EPIC Images

Satellite images often feature sun glints caused by the specular reflection of sunlight from water surfaces or from horizontally oriented ice crystals occurring in clouds. Such glints can prevent accurate retrievals of atmospheric and surface properties using existing algorithms, but the glints can also be used to infer more about the glint-causing objects—for example about the microphysical properties and radiative effects of ice clouds. This paper introduces the recently released operational glint product of the Earth Polychromatic Camera (EPIC) onboard the Deep Space Climate Observatory (DSCOVR) spacecraft. Most importantly, the paper describes the algorithm used for generating the key component of the new product: a glint mask indicating the presence of sun glint caused by the specular reflection of sunlight from ice clouds and smooth water surfaces. After describing the glint detection algorithm and glint product, the paper shows some examples of the detected glints and discusses some basic statistics of the glint population in a yearlong dataset of EPIC images. These statistics provide insights into the performance of glint detection and point toward possibilities for using the glint product to gain scientific insights about ice clouds and water surfaces

Terrestrial glint seen from deep space: Oriented ice crystals detected from the Lagrangian point

The Deep Space Climate Observatory (DSCOVR) spacecraft resides at the first Lagrangian point about one million miles from Earth. A polychromatic imaging camera onboard delivers nearly hourly observations of the entire sunlit face of the Earth. Many images contain unexpected bright flashes of light over both ocean and land. We construct a yearlong time series of flash latitudes, scattering angles, and oxygen absorption to demonstrate conclusively that the flashes over land are specular reflections off tiny ice platelets floating in the air nearly horizontally. Such deep space detection of tropospheric ice can be used to constrain the likelihood of oriented crystals and their contribution to Earth albedo. These glint observations also support proposals for detecting starlight glints off faint companions in our search for habitable exoplanets

Reversible record breaking and variability: Temperature distributions across the globe

Based on counts of record highs and lows, and employing reversibility in time, an approach to examining natural variability is proposed. The focus is on intrinsic variability; that is, variance separated from the trend in the mean. A variability index α is suggested and studied for an ensemble of monthly temperature time series around the globe. Deviation of 〈α〉 (mean α) from zero, for an ensemble of time series, signifies a variance trend in a distribution-independent manner. For 15 635 monthly temperature time series from different geographical locations (Global Historical Climatology Network), each time series about a century-long, 〈α〉 = −1.0, indicating decreasing variability. This value is an order of magnitude greater than the 3σ value of stationary simulations. Using the conventional best-fit Gaussian temperature distribution, the trend is associated with a change of about −0.2°C (106 yr)−1 in the standard deviation of interannual monthly mean temperature distributions (about 10%)

Universal rank-order transform to extract signals from noisy data

We introduce an ordinate method for noisy data analysis, based solely on rank information and thus insensitive to outliers. The method is nonparametric and objective, and the required data processing is parsimonious. The main ingredients include a rank-order data matrix and its transform to a stable form, which provide linear trends in excellent agreement with least squares regression, despite the loss of magnitude information. A group symmetry orthogonal decomposition of the 2D rank-order transform for iid (white) noise is further ordered by principal component analysis. This two-step procedure provides a noise “etalon” used to characterize arbitrary stationary stochastic processes. The method readily distinguishes both the Ornstein-Uhlenbeck process and chaos generated by the logistic map from white noise. Ranking within randomness differs fundamentally from that in deterministic chaos and signals, thus forming the basis for signal detection. To further illustrate the breadth of applications, we apply this ordinate method to the canonical nonlinear parameter estimation problem of two-species radioactive decay, outperforming special-purpose least squares software. We demonstrate that the method excels when extracting trends in heavy-tailed noise and, unlike the Thiele-Sen estimator, is not limited to linear regression. A simple expression is given that yields a close approximation for signal extraction of an underlying, generally nonlinear signal