Abstract. Palaeoclimatic information can be retrieved from the diffusion of the stable water isotope signal during firnification of snow. The diffusion length, a measure for the amount of diffusion a layer has experienced, depends on the firn temperature and the accumulation rate. We show that the estimation of the diffusion length using power spectral densities (PSDs) of the record of a single isotope species can be biased by uncertainties in spectral properties of the isotope signal prior to diffusion. By using a second water isotope and calculating the difference in diffusion lengths between the two isotopes, this problem is circumvented. We study the PSD method applied to two isotopes in detail and additionally present a new forward diffusion method for retrieving the differential diffusion length based on the Pearson correlation between the two isotope signals. The two methods are discussed and extensively tested on synthetic data which are generated in a Monte Carlo manner. We show that calibration of the PSD method with this synthetic data is necessary to be able to objectively determine the differential diffusion length. The correlation-based method proves to be a good alternative for the PSD method as it yields precision equal to or somewhat higher than the PSD method. The use of synthetic data also allows us to estimate the accuracy and precision of the two methods and to choose the best sampling strategy to obtain past temperatures with the required precision. In addition to application to synthetic data the two methods are tested on stable-isotope records from the EPICA (European Project for Ice Coring in Antarctica) ice core drilled in Dronning Maud Land, Antarctica, showing that reliable firn temperatures can be reconstructed with a typical uncertainty of 1.5 and 2 • C for the Holocene period and 2 and 2.5 • C for the last glacial period for the correlation and PSD method, respectively.

Palaeoclimatic information can be retrieved from the diffusion of the stable water isotope signal during firnification of snow. The diffusion length, a measure for the amount of diffusion a layer has experienced, depends on the firn temperature and the accumulation rate. We show that the estimation of the diffusion length using power spectral densities (PSDs) of the record of a single isotope species can be biased by uncertainties in spectral properties of the isotope signal prior to diffusion. By using a second water isotope and calculating the difference in diffusion lengths between the two isotopes, this problem is circumvented. We study the PSD method applied to two isotopes in detail and additionally present a new forward diffusion method for retrieving the differential diffusion length based on the Pearson correlation between the two isotope signals. The two methods are discussed and extensively tested on synthetic data which are generated in a Monte Carlo manner. We show that calibration of the PSD method with this synthetic data is necessary to be able to objectively determine the differential diffusion length. The correlation-based method proves to be a good alternative for the PSD method as it yields precision equal to or somewhat higher than the PSD method. The use of synthetic data also allows us to estimate the accuracy and precision of the two methods and to choose the best sampling strategy to obtain past temperatures with the required precision. In addition to application to synthetic data the two methods are tested on stable-isotope records from the EPICA (European Project for Ice Coring in Antarctica) ice core drilled in Dronning Maud Land, Antarctica, showing that reliable firn temperatures can be reconstructed with a typical uncertainty of 1.5 and 2 • C for the Holocene period and 2 and 2.5 • C for the last glacial period for the correlation and PSD method, respectively.

In the future, advanced multi-energy systems are expected to handle an increasing share of fluctuating renewable energy generation through the management of multiple advanced energy conversion and storage technologies operating across different energy carriers. The market diffusion of such concepts of Local Energy Management—the management of energy supply, demand, and storage within a given geographical area—is expected to provoke a fundamental reorganization of the power generation sector. This work contributes to this topic by estimating the maximum potential economic value attained from using the flexibility of a district to take advantage of operating within multiple electricity markets at the same time. The study is based on the measured demand and production data of a newly built suburban residential district located in Central Switzerland. The actual configuration of the district and the resulting flexibility, as well as an extension with a battery storage system, is used to estimate the economic value of the flexibility. Then, an optimization algorithm manages flexible demand, production, and storage capacities in order to alternatively maximize the revenues/cost savings, self-sufficiency, or share of renewable resources of the district’s energy supply. In this vein, the impact of the way the system operates in the markets regarding the degradation of the battery is assessed and its pay-back-time is estimated. The analysis revealed a considerable profit potential associated with the district thermal and electricity storage flexibility, in particular, when operating on both the spot and reserve electricity markets. Firstly, it was shown that overall energy costs can be minimized through an optimal management of energy conversion and storage systems. Secondly, complementing the infrastructure with batteries and trading flexibility on the spot market would decrease costs by about 43%, while an additional 20% cost decrease could be captured by including trading on the reserve market. Thirdly, it has been shown that operation on the spot- and reserve market does not seem to degrade the battery more than solely operation on the spot market. However, when operating on the spot- and reserve markets, battery amortization would still take about 10 years.