Spatial and Temporal Variations in Active Layer Thawing and Their Implication on Runoff Generation in Peat-Covered Permafrost Terrain

The distribution of frost table depths on a peat-covered permafrost slope was examined in a discontinuous permafrost region in northern Canada over 4 consecutive years at a variety of spatial scales, to elucidate the role of active layer development on runoff generation. Frost table depths were highly variable over relatively short distances (0.25–1 m), and the spatial variability was strongly correlated to soil moisture distribution, which was partly influenced by lateral flow converging to frost table depressions. On an interannual basis, thaw rates were temporally correlated to air temperature and the amount of precipitation input. Simple simulations show that lateral subsurface flow is governed by the frost table topography having spatially variable storage that has to be filled before water can spill over to generate flow downslope, in a similar manner that bedrock topography controls subsurface flow. However, unlike the bedrock surface, the frost table is variable with time and strongly influenced by the heat transfer involving water. Therefore, it is important to understand the feedback between thawing and subsurface water flow and to properly represent the feedback in hydrological models of permafrost regions

Statistical mechanical evaluation of spread spectrum watermarking model with image restoration

In cases in which an original image is blind, a decoding method where both the image and the messages can be estimated simultaneously is desirable. We propose a spread spectrum watermarking model with image restoration based on Bayes estimation. We therefore need to assume some prior probabilities. The probability for estimating the messages is given by the uniform distribution, and the ones for the image are given by the infinite range model and 2D Ising model. Any attacks from unauthorized users can be represented by channel models. We can obtain the estimated messages and image by maximizing the posterior probability. We analyzed the performance of the proposed method by the replica method in the case of the infinite range model. We first calculated the theoretical values of the bit error rate from obtained saddle point equations and then verified them by computer simulations. For this purpose, we assumed that the image is binary and is generated from a given prior probability. We also assume that attacks can be represented by the Gaussian channel. The computer simulation retults agreed with the theoretical values. In the case of prior probability given by the 2D Ising model, in which each pixel is statically connected with four-neighbors, we evaluated the decoding performance by computer simulations, since the replica theory could not be applied. Results using the 2D Ising model showed that the proposed method with image restoration is as effective as the infinite range model for decoding messages. We compared the performances in a case in which the image was blind and one in which it was informed. The difference between these cases was small as long as the embedding and attack rates were small. This demonstrates that the proposed method with simultaneous estimation is effective as a watermarking decoder