Hydrologic models for land-atmosphere retrospective studies of the use of LANDSAT and AVHRR data

The use of a Geographic Information System (GIS) and LANDSAT analysis in conjunction with the Simulator for Water Resources on a Rural Basin (SWRRB) hydrologic model to examine the water balance on the Little Washita River basin is discussed. LANDSAT analysis was used to divide the basin into eight non-contiguous land covers or subareas: rangeland, grazed range, winter wheat, alfalfa/pasture, bare soil, water, woodland, and impervious land (roads, quarry). The use of a geographic information system allowed for the calculation of SWRRB model parameters in each subarea. Four data sets were constructed in order to compare SWRRB estimates of hydrologic processes using two methods of maximum LAI and two methods of watershed subdivision. Maximum LAI was determined from a continental scale map, which provided a value of 4.5 for the entire basin, and from its association with the type of land-cover (eight values). The two methods of watershed subdivision were determined according to drainage subbasin (four) and the eight land-covers. These data sets were used with the SWRRB model to obtain daily hydrologic estimates for 1985. The results of the one year analysis lead to the conclusion that the greater homogeneity of a land-cover subdivision provides better water yield estimates than those based on a drainage properties subdivision

Coordinated field study for CaPE: Analysis of energy and water budgets

The objectives of this hydrologic cycle study are to understand and model (1) surface energy and land-atmosphere water transfer processes, and (2) interactions between convective storms and surface energy fluxes. A surface energy budget measurement campaign was carried out by an interdisciplinary science team during the period July 8 - August 19, 1991 as part of the Convection and Precipitation/Electrification Experiment (CaPE) in the vicinity of Cape Canaveral, FL. Among the research themes associated with CaPE is the remote estimation of rainfall. Thus, in addition to surface radiation and energy budget measurements, surface mesonet, special radiosonde, precipitation, high-resolution satellite (SPOT) data, geosynchronous (GOES) and polar orbiting (DMSP SSM/I, OLS; NOAA AVHRR) satellite data, and high altitude airplane data (AMPR, MAMS, HIS) were collected. Initial quality control of the seven surface flux station data sets has begun. Ancillary data sets are being collected and assembled for analysis. Browsing of GOES and radar data has begun to classify days as disturbed/undisturbed to identify the larger scale forcing of the pre-convective environment, convection storms and precipitation. The science analysis plan has been finalized and tasks assigned to various investigators

Simple Systems with Anomalous Dissipation and Energy Cascade

We analyze a class of linear shell models subject to stochastic forcing in finitely many degrees of freedom. The unforced systems considered formally conserve energy. Despite being formally conservative, we show that these dynamical systems support dissipative solutions (suitably defined) and, as a result, may admit unique (statistical) steady states when the forcing term is nonzero. This claim is demonstrated via the complete characterization of the solutions of the system above for specific choices of the coupling coefficients. The mechanism of anomalous dissipations is shown to arise via a cascade of the energy towards the modes ($a_n$) with higher $n$; this is responsible for solutions with interesting energy spectra, namely \EE |a_n|^2 scales as $n^{-\alpha}$ as $n\to\infty$. Here the exponents $\alpha$ depend on the coupling coefficients $c_n$ and \EE denotes expectation with respect to the equilibrium measure. This is reminiscent of the conjectured properties of the solutions of the Navier-Stokes equations in the inviscid limit and their accepted relationship with fully developed turbulence. Hence, these simple models illustrate some of the heuristic ideas that have been advanced to characterize turbulence, similar in that respect to the random passive scalar or random Burgers equation, but even simpler and fully solvable.Comment: 32 Page

Area distribution of the planar random loop boundary

We numerically investigate the area statistics of the outer boundary of planar random loops, on the square and triangular lattices. Our Monte Carlo simulations suggest that the underlying limit distribution is the Airy distribution, which was recently found to appear also as area distribution in the model of self-avoiding loops.Comment: 10 pages, 2 figures. v2: minor changes, version as publishe

Macroscopic models for superconductivity

This paper reviews the derivation of some macroscopic models for superconductivity and also some of the mathematical challenges posed by these models. The paper begins by exploring certain analogies between phase changes in superconductors and those in solidification and melting. However, it is soon found that there are severe limitations on the range of validity of these analogies and outside this range many interesting open questions can be posed about the solutions to the macroscopic models

Gaussian multiplicative Chaos for symmetric isotropic matrices

Motivated by isotropic fully developed turbulence, we define a theory of symmetric matrix valued isotropic Gaussian multiplicative chaos. Our construction extends the scalar theory developed by J.P. Kahane in 1985

Scaling prediction for self-avoiding polygons revisited

We analyse new exact enumeration data for self-avoiding polygons, counted by perimeter and area on the square, triangular and hexagonal lattices. In extending earlier analyses, we focus on the perimeter moments in the vicinity of the bicritical point. We also consider the shape of the critical curve near the bicritical point, which describes the crossover to the branched polymer phase. Our recently conjectured expression for the scaling function of rooted self-avoiding polygons is further supported. For (unrooted) self-avoiding polygons, the analysis reveals the presence of an additional additive term with a new universal amplitude. We conjecture the exact value of this amplitude.Comment: 17 pages, 3 figure

Opportunities for use of exact statistical equations

Exact structure function equations are an efficient means of obtaining asymptotic laws such as inertial range laws, as well as all measurable effects of inhomogeneity and anisotropy that cause deviations from such laws. "Exact" means that the equations are obtained from the Navier-Stokes equation or other hydrodynamic equations without any approximation. A pragmatic definition of local homogeneity lies within the exact equations because terms that explicitly depend on the rate of change of measurement location appear within the exact equations; an analogous statement is true for local stationarity. An exact definition of averaging operations is required for the exact equations. Careful derivations of several inertial range laws have appeared in the literature recently in the form of theorems. These theorems give the relationships of the energy dissipation rate to the structure function of acceleration increment multiplied by velocity increment and to both the trace of and the components of the third-order velocity structure functions. These laws are efficiently derived from the exact velocity structure function equations. In some respects, the results obtained herein differ from the previous theorems. The acceleration-velocity structure function is useful for obtaining the energy dissipation rate in particle tracking experiments provided that the effects of inhomogeneity are estimated by means of displacing the measurement location.Comment: accepted by Journal of Turbulenc