We investigate evaporative lithography as a route for patterning colloidal films. Films are dried beneath a mask that induces periodic variations between regions of free and hindered evaporation. Direct imaging reveals that particles segregate laterally within the film, as fluid and entrained particles migrate towards regions of higher evaporative flux. The films exhibit remarkable pattern formation that can be regulated by tuning the initial suspension composition, separation distance between the mask and underlying film, and mask geometry.

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Small-scale (less than ϳ15 km) precipitation variability significantly affects the hydrologic response of a basin and the accurate estimation of water and energy fluxes through coupled land-atmosphere modeling schemes. It also affects the radiative transfer through precipitating clouds and thus rainfall estimation from microwave sensors. Because both land-atmosphere and cloud-radiation interactions are nonlinear and occur over a broad range of scales (from a few centimeters to several kilometers), it is important that, over these scales, cloudresolving numerical models realistically reproduce the observed precipitation variability. This issue is examined herein by using a suite of multiscale statistical methods to compare the scale dependence of precipitation variability of a numerically simulated convective storm with that observed by radar. In particular, Fourier spectrum, structure function, and moment-scale analyses are used to show that, although the variability of modeled precipitation agrees with that observed for scales larger than approximately 5 times the model resolution, the model shows a falloff in variability at smaller scales. Thus, depending upon the smallest scale at which variability is considered to be important for a specific application, one has to resort either to very high resolution model runs (resolutions 5 times higher than the scale of interest) or to stochastic methods that can introduce the missing small-scale variability. The latter involve upscaling the model output to a scale approximately 5 times the model resolution and then stochastically downscaling it to smaller scales. The results of multiscale analyses, such as those presented herein, are key to the implementation of such stochastic downscaling methodologies.

Data from networks of high time resolution (15 second) rain gauges forming a transect from the base to the divide of a mountain range are used to study the multifractal characteristics of precipitation at different locations along the transect. In particular, scaling power spectra, multiscaling moments and power law exceedence probability tails are analyzed from rain gauge time series of ∼35–70 hours in length. The parameters discussed are specifically the spectral scaling exponent, β, the intermittency parameter, C1 (a fundamental parameter of the moment scaling function, K(q)) and qcr, the power law probability tail exponent. Results show a systematic trend in the exponents, indicating a decrease in intermittency, the frequency of extreme values and smoothness of the time series with increasing altitude along the transect. K(q) and qcr are briefly discussed and derived as natural properties of multifractal cascades. It is concluded that the parameters of multifractal cascade models of rainfall are related to the physical processes which are qualitatively discussed in the context of the observed changes in the statistics.

Abstract. The connection among different types of exponents characterizing multiscaling properties of rainfall and a criterion for stationarity of random fields are discussed, and a new phenomenological model for rainfall time series simulation is proposed. The bounded random cascade model presented here is a generalization of the well-known a model with the multiplicative weights of the generator converging to unity as the cascade proceeds to smaller scales. This allows one to directly simulate a multiscaling random field with an energy spectrum exponent, •3 > 1, which is typical for rainfall time series data but which cannot be produced by a standard a model. A procedure is proposed for estimating the cascade parameters of this new bounded a model from observed data. Parameters are estimated from two data sets with different degrees of intermittency and different spectral exponents. The bounded a model simulations using these parameters produced realistic rainfall time series with spectral exponents similar to their observed counterparts. We expect that the occurrence of rainfall and turbulence have something in common since rain is a tracer of turbulence at small scales and the larger eddies may be involved in the processes which produce rainfall. This suggests the two phenomena might be described by the same models. However, we believe it is clear that the physical processes which produce large areas of uniform rain and small convective showers, for example, are radically different and are extremely unlikely to be described as different realizations of a random multiplicative cascade with the same parameters. In our view the best justification for the use of the multiplicative cascade models in rainfall pattern analysis is the remarkable ability of the technique to reproduce the observed structure of rainfall patterns and its statistical properties. We therefore believe that the careful analysis of the goodness of fit of the statistical properties of the simulated pattern with the observed one is actually crucial, especially taking into account the phenomenological character of the cascade models. As already mentioned, /3 is an important exponent in classifying whether an observed field can be modeled by a bounded or unbounded cascade depending on whether/3 > 1 or/3 < 1, respectively. This condition on/3 has often been related to the stationarity of a field. However, we show that this is not the only possible interpretation and illustrate the point with a counterexample of a stationary random process with scaling energy spectrum with /3 > 1. Another important result that follows from this counterexample is that the condition/3 > 1 implies that the moments of the raw field do not scale, and thus K(q) function is not defined. When using discrete cascades to model rainfall (and many other geophysical fields) one runs into the familiar problemSection 3 presents a new type of bounded cascade along with a parameter estimation method for the model from real data.As an applicatioh, the bounded a model parameters are...