Higher-Order Allan Variance for Atomic Clocks of Arbitrary Order

In this paper, we perform a time-domain analysis of the higher-order Allan variance for atomic clock models of arbitrary order. Adopting a standard atomic clock model where the time series of the clock reading deviation is expressed as a Wiener or integrated Wiener process, we define the higher-order Allan variance as the mean squared higher-order difference of the clock reading deviation. The main results of this paper are threefold. First, we prove that the higher-order difference operation of the clock reading deviation, which can be interpreted as a linear aggregation with binomial coefficients, is not only sufficient, but also necessary for a resulting aggregated time series to be an independent and identically distributed Gaussian process. Second, we derive a complete analytical expression of the higher-order Allan variance, which consists of both time-dependent and time-independent terms. Third and finally, we prove that the higher-order Allan variance is time-independent if and only if the order of difference operation is greater than or equal to the order of the atomic clock model

Evaluation of Precipitation Estimates by at-Launch Codes of GPM/DPR Algorithms Using Synthetic Data from TRMM/PR Observations

The Global Precipitation Measurement (GPM) Core Observatory will carry a Dual-frequency Precipitation Radar (DPR) consisting of a Ku-band precipitation radar (KuPR) and a Ka-band precipitation radar (KaPR). In this study, \u27at-launch\u27 codes of DPR precipitation algorithms, which will be used in GPM ground systems at launch, were evaluated using synthetic data based upon the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR) data. Results from the codes (Version 4.20131010) of the KuPR-only, KaPR-only, and DPR algorithms were compared with \u27true values\u27 calculated based upon drop size distributions assumed in the synthetic data and standard results from the TRMM algorithms at an altitude of 2 km over the ocean. The results indicate that the total precipitation amounts during April 2011 from the KuPR and DPR algorithms are similar to the true values, whereas the estimates from the KaPR data are underestimated. Moreover, the DPR estimates yielded smaller precipitation rates for rates less than about 10 mm/h and greater precipitation rates above 10 mm/h. Underestimation of the KaPR estimates was analyzed in terms of measured radar reflectivity ({\bf Z}-{\bf m}) of the KaPR at an altitude of 2 km. The underestimation of the KaPR data was most pronounced during strong precipitation events of {\bf Z}-{\bf m} \lt {\bf 18}~{\bf dBZ} (high attenuation cases) over heavy precipitation areas in the Tropics, whereas the underestimation was less pronounced when the {\bf Z}-{\bf m}\gt 26~{\bf dBZ} (moderate attenuation cases). The results suggest that the underestimation is caused by a problem in the attenuation correction method, which was verified by the improved codes

Scandinavian IMS magnetometer array data and their use for studies ofgeomagnetic rapid variations

A data set which was newly open to the public from the World Data Center C2 for Geomagnetism is introduced. It was obtained from geomagnetic observations at 36 stations in Scandinavia during the International Magnetospheric Study (1977-1979). A few examples of analysis using the data are shown

原子時系発生システムの高度化に関する研究

An atomic time scale is a time scale generated by an atomic clock. In practice, anatomic time scale is usually obtained by averaging many atomic clocks within a specialgenerating system. Quality of hardware and methodology of data processing of thissystem directly affect on the quality of the time scale.In this study, we present a combined solution of upgrading a generating system ofatomic time scale through improvements of a Japan Standard Time (JST) generatingsystem. There are two aspects for improving a JST generating system, that is, hardwareimprovement and software improvement. In hardware improvement, we developed anew generating system, while in software improvement, we investigated and improve atime scale algorithm which is of how to compute JST time scale from several atomicclocks.The presented solution is with a new JST generating system and includes variousupgrading. First, hydrogen masers were introduced for improving short-term frequencystability. Second, a newly developed measurement device achieves extremely highmeasurement precision. Moreover, a data processing program automatically removesdata from a measurement device that works in unfavorable conditions. This new JSTsystem started a regular operation in 2006. We confirmed that quality of JST washighly improved by this new system.To improve the JST time scale algorithm, unexpected large rate changes of JSTtime scale were investigated and solved. In our approach, we investigated their causesby checking the equations of time scale algorithm. After determining the causes,solutions were searched both theoretically and by simulations. As a result, we foundthe solutions for each problem and confirmed their efficiency by computer simulation.In conclusion, using the proposed solution, we highly improved Japan StandardTime system and achieved an atomic time scale with high quality.電気通信大学200