Potential and scientific requirements of optical clock networks for validating satellite gravity missions

<p>The GRACE mission, now continued as the GRACE-FO mission, has provided an unprecedented quantification of large-scale changes in the water cycle.<br>Meanwhile, stationary optical clocks show fractional instabilities below 10<sup>-18</sup> when averaged over an hour, and continue to be improved in terms of precision and accuracy, uptime, and transportability. The frequency of a clock is affected by the gravitational redshift, and thus depends on the local geopotential; a relative frequency change of 10<sup>-18</sup> corresponds to a geoid height change of about 1 cm. This effect could be exploited for sensing temporal geopotential changes via a network of clocks distributed at the Earth's surface. <br>Here, we concentrate on how the measurements of an ensemble of optical clocks connected accross Europe via optical fibre links could be used to validate and complement gravity field solutions from GRACE-FO and potential future gravity missions.<br>Through simulations it is shown how hydrology (water storage) and atmosphere (dry and wet air mass) variations over Europe could be observed with clock comparisons in a future network. We assume different scenarios for clock and GNSS uncertainties, where we deem the latter to be nessecary to separate local height changes from the mass redistribution signals. Our findings suggest that even under conservative assumptions -- a clock error of 10<sup>-18</sup> and vertical height control error of 1.4 mm for daily measurements -- hydrological signals at the annual time scale and atmospheric signals down to the weekly time scale could be observed.<br>However, the requirements to an optical clock network used for validation of GRACE-FO and future gravity missions are higher than that, which is demonstrated along with the according spatial resolutions.</p>

Clock networks and their sensibility to time-variable gravity signals

<p>High-performance clock networks are considered as a novel tool in geodesy. Today the latest generation of optical clocks approaches a fractional frequency uncertainty of 1.0x10<sup>-18</sup>, which corresponds to about 1.0 cm in height or 0.1 m<sup>2</sup>/s<sup>2</sup> in geopotential. The connected clocks are thus promising to enable “relativistic geodesy” in practice: Gravity potential (or height) differences can be inferred through the ultra-precise comparison of clocks’ frequencies.</p><p>In this study, we will investigate the possibility of high-performance clock networks for detecting time-variable gravity signals. In the past two decades, the satellite gravity mission GRACE, now continued by its follow-on mission, has significantly improved our knowledge on the Earth’s gravity field, especially on its changes over time. However, the results are limited in terms of spatial resolution (about a few hundreds of kilometers) and temporal resolution (standard is one month). Terrestrial clock networks can be used to observe point-wise gravity potential values at locations of interest. By continuously tracking of changes w.r.t. a reference clock, time-series of gravity potential values are obtained, which reveal the gravity variations at these locations. To elaborate this idea, we will address the following research questions:</p><ul><li>Are clock measurements with the accuracy of 10<sup>-18</sup> sensitive enough to time-variable gravity signals? Or what is the requirement on the clock’s performance for detecting time-variable gravity signals?</li> <li>Which kinds of time-variable signals can be “seen” by clocks, the long-term trends (yearly), seasonal variations or short-term changes (weekly/daily)?</li> <li>In which regions might clock networks be sensitive to time-variable gravity signals, in Amazon, Greenland or also in Europe?</li> <li>An “absolute” reference clock is required for a network that should be least affected by gravity variations. Where should it be placed?</li> </ul><p>We gratefully acknowledge the financial support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC-2123 “QuantumFrontiers” (Project-ID: 390837967). This work is also funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project-ID 434617780 – SFB 1464.</p>

Model and Non-model Insects in Chronobiology

The fruit fly Drosophila melanogaster is an established model organism in chronobiology, because genetic manipulation and breeding in the laboratory are easy. The circadian clock neuroanatomy in D. melanogaster is one of the best-known clock networks in insects and basic circadian behavior has been characterized in detail in this insect. Another model in chronobiology is the honey bee Apis mellifera, of which diurnal foraging behavior has been described already in the early twentieth century. A. mellifera hallmarks the research on the interplay between the clock and sociality and complex behaviors like sun compass navigation and time-place-learning. Nevertheless, there are aspects of clock structure and function, like for example the role of the clock in photoperiodism and diapause, which can be only insufficiently investigated in these two models. Unlike high-latitude flies such as Chymomyza costata or D. ezoana, cosmopolitan D. melanogaster flies do not display a photoperiodic diapause. Similarly, A. mellifera bees do not go into “real” diapause, but most solitary bee species exhibit an obligatory diapause. Furthermore, sociality evolved in different Hymenoptera independently, wherefore it might be misleading to study the social clock only in one social insect. Consequently, additional research on non-model insects is required to understand the circadian clock in Diptera and Hymenoptera. In this review, we introduce the two chronobiology model insects D. melanogaster and A. mellifera, compare them with other insects and show their advantages and limitations as general models for insect circadian clocks.

Effect of integrated power and clock networks on combinational circuits

<p class="western" align="JUSTIFY"><span style="font-size: small;"><span style="color: #000000;"><span style="font-family: 'Times New Roman', serif;"><span><span>Reduction of power consumption is necessary in a system on chip. To achieve this, power and clock networks can be integrated. This leads to a significant reduction in power consumption in a circuit. This paper explores the effect of such a network on various combinational circuits and compares the power consumption of these circuits with conventional combinational circuits. The combinational circuits which are powered by the proposed circuit consume lesser power as compared to conventional combinational circuits.</span></span></span></span></span></p>

Validating future gravity missions via optical clock networks

&lt;p&gt;Stationary optical clocks show fractional instabilities below 10&lt;sup&gt;-18&lt;/sup&gt; when averaged over an hour, and continue to be improved in terms of precision and accuracy, uptime and transportability. The frequency of a clock is affected by the gravitational redshift, and thus depends on the local geopotential; a relative frequency change of 10&lt;sup&gt;-18&lt;/sup&gt; corresponds to a geoid height change of about 1 cm. This effect could be exploited for sensing large-scale temporal geopotential changes via a network of clocks distributed at the Earth's surface. The CLOck NETwork Services (CLONETS) project aims to create an ensemble of optical clocks connected across Europe via optical fibre links.&lt;br&gt;A station network spread over Europe, which is already installed in parts, would enable us to determine temporal variations of the Earth's gravity field at time scales of days &amp;#160;and thus provide a new means for validating satellite missions such as GRACE-FO or potential Next Generation Gravity Missions. However, mass changes at the surface of an elastic Earth are accompanied by load-induced height changes, and clocks are sensitive to non-loading e.g. tectonic height changes as well. As a result, local and global mass redistribution as well as local height change will be entangled in clock readings, and very precise&amp;#160; GNSS measurements will be required to separate them.&lt;br&gt;Here, we show through simulations how ice (glacier mass imbalance), hydrology (water storage) and atmosphere (dry and wet air mass) signals over Europe could be observed with the currently proposed/established clock network geometry and how potential extensions can benefit this observability. The importance of collocated GNSS receivers is demonstrated for the sake of signal separation.&lt;/p&gt;