Unification of the probe and singular sources methods for the inverse boundary value problem by the no-response test

In this article, we use the no-response test idea, introduced in Luke and Potthast (2003) and Potthast (Preprint) and the inverse obstacle problem, to identify the interface of the discontinuity of the coefficient gamma of the equation del (.) gamma(x)del + c(x) with piecewise regular gamma and bounded function c(x). We use infinitely many Cauchy data as measurement and give a reconstructive method to localize the interface. We will base this multiwave version of the no-response test on two different proofs. The first one contains a pointwise estimate as used by the singular sources method. The second one is built on an energy (or an integral) estimate which is the basis of the probe method. As a conclusion of this, the probe and the singular sources methods are equivalent regarding their convergence and the no-response test can be seen as a unified framework for these methods. As a further contribution, we provide a formula to reconstruct the values of the jump of gamma(x), x is an element of partial derivative D at the boundary. A second consequence of this formula is that the blow-up rate of the indicator functions of the probe and singular sources methods at the interface is given by the order of the singularity of the fundamental solution.

Estimating drizzle drop size and precipitation rate using two-colour lidar measurements

A method to estimate the size and liquid water content of drizzle drops using lidar measurements at two wavelengths is described. The method exploits the differential absorption of infrared light by liquid water at 905 nm and 1.5 μm, which leads to a different backscatter cross section for water drops larger than ≈50 μm. The ratio of backscatter measured from drizzle samples below cloud base at these two wavelengths (the colour ratio) provides a measure of the median volume drop diameter D0. This is a strong effect: for D0=200 μm, a colour ratio of ≈6 dB is predicted. Once D0 is known, the measured backscatter at 905 nm can be used to calculate the liquid water content (LWC) and other moments of the drizzle drop distribution. The method is applied to observations of drizzle falling from stratocumulus and stratus clouds. High resolution (32 s, 36 m) profiles of D0, LWC and precipitation rate R are derived. The main sources of error in the technique are the need to assume a value for the dispersion parameter μ in the drop size spectrum (leading to at most a 35% error in R) and the influence of aerosol returns on the retrieval (≈10% error in R for the cases considered here). Radar reflectivities are also computed from the lidar data, and compared to independent measurements from a colocated cloud radar, offering independent validation of the derived drop size distributions.

A double data rate (DDR) architecture for OFDM based wireless consumer devices

The creation of OFDM based Wireless Personal Area Networks (WPANs) has allowed the development of high bit-rate wireless communication devices suitable for streaming High Definition video between consumer products, as demonstrated in Wireless-USB and Wireless-HDMI. However, these devices need high frequency clock rates, particularly for the OFDM, FFT and symbol processing sections resulting in high silicon cost and high electrical power. The high clock rates make hardware prototyping difficult and verification is therefore very important but costly. Acknowledging that electrical power in wireless consumer devices is more critical than the number of implemented logic gates, this paper presents a Double Data Rate (DDR) architecture for implementation inside a OFDM baseband codec in order to reduce the high frequency clock rates by a complete factor of 2. The presented architecture has been implemented and tested for ECMA-368 (Wireless- USB context) resulting in a maximum clock rate of 264MHz instead of the expected 528MHz clock rate existing anywhere on the baseband codec die.

A double data rate (DDR) architecture for OFDM based wireless consumer devices

The creation of OFDM based Wireless Personal Area Networks (WPANs) has allowed high bit-rate wireless communication devices suitable for streaming High Definition video between consumer products as demonstrated in Wireless- USB. However, these devices need high clock rates, particularly for the OFDM sections resulting in high silicon cost and high electrical power. Acknowledging that electrical power in wireless consumer devices is more critical than the number of implemented logic gates, this paper presents a Double Data Rate (DDR) architecture to reduce the OFDM input and output clock rate by a factor of 2. The architecture has been implemented and tested for Wireless-USB (ECMA-368) resulting in a maximum clock of 264MHz instead of 528MHz existing anywhere on the die.

CISK or WISHE as the mechanism for tropical cyclone intensification

Examination of conditional instability of the second kind (CISK) and wind-induced surface heat exchange (WISHE), two proposed mechanisms for tropical cyclone and polar low intensification, suggests that the sensitivity of the intensification rate of these disturbances to surface properties, such as surface friction and moisture supply, will be different for the two mechanisms. These sensitivities were examined by perturbing the surface characteristics in a numerical model with explicit convection. The intensification rate was found to have a strong positive dependence on the heat and moisture transfer coefficients, while remaining largely insensitive to the frictional drag coefficient. CISK does not predict the observed dependence of vortex intensification rate on the heat and moisture transfer coefficients, nor the insensitivity to the frictional drag coefficient since it anticipates that intensification rate is controlled by frictional convergence in the boundary layer. Since neither conditional instability nor boundary moisture content showed any significant sensitivity to the transfer coefficients, this is true of CISK using both the convective closures of Ooyama and of Charney and Eliassen. In comparison, the WISHE intensification mechanism does predict the observed increase in intensification rate with heat and moisture transfer coefficients, while not anticipating a direct influence from surface friction.

Decadal-scale rainfall variability in Ethiopia recorded in an annually laminated, Holocene-age, stalagmite

An annually laminated, uranium-series dated, Holocene stalagmite from southeast Ethiopia has been analysed for growth rate and δ13C and δ18O variations at annual to biennial resolution, in order to provide the first long duration proxy record of decadal-scale rainfall variability in this climatically sensitive region. Our study site (10°N) is climatically influenced by both summer (June—August) and spring (March—May) rainfall caused by the annual movement of the Inter-Tropical Convergence Zone (ITCZ) and modulated by large-scale anomalies in the atmospheric circulation and in ocean temperatures. Here we show that stalagmite growth, episodic throughout the last 7800 years, demonstrates decadal-scale (8—25 yr) variability in both growth rate and δ 18O. A hydrological model was employed and indicates that this decadal variability is due to variations in the relative amounts of rainfall in the two rain seasons. Our record, unique in its combination of length (a total of ~1000 years), annual chronology and high resolution δ18O, shows for the first time that such decadal-scale variability in rainfall in this region has occurred through the Holocene, which implies persistent decadal-scale variability for the large-scale atmospheric and oceanic driving factors.