Check this link guys, its by varta, tells you exactly what kind of battery is needed for all types of cars. After searching mine, it seems that Mr Wilks did choose his battery type correctly!

On the other hand it also gives a second recommended battery which is 80AH and 800CCA. So I dont really think one has to replace the battery with a new one of the exact same specifications.
https://www.varta-automotive.com/en-gb/battery-finder?type=pc&year=2011&make=16&model=8033&engine=31018&etn=580+901+080%7C570+901+076%7C&rec_etn=570+901+076%7C&ss_etn=580+901+080%7C570+901+076%7C&literal_search=%7B%22type%22%3A%22Passenger+Car%22%2C%22year%22%3A%222011%22%2C%22make%22%3A%22BMW%22%2C%22model%22%3A%22Z4+Roadster+%28E89%29%22%2C%22engine%22%3A%22sDrive+30+i+%28190+kW+%2F+258+PS%29%22%7D