There's currently no failproof and scientifically proven way to guarantee 30+ years of cold data archival. But some projects are aiming to do that like the Rosetta Disks project of the Long Now museum, although they are still very costly and with a low data density (about 50 MB).
In the meantime, you can use scientifically proven resilient optical mediums for cold storage like archival grade DVD+R like Verbatim Gold Archival, or better, BluRay Discs of HTL type like Panasonic's, and keep them in water-tight boxes in a soft spot (avoid high temperature) and out of the light. Make multiple copies of your data, and compute hashes to check regularly that everything is alright, and every few years you should rewrite your data on new disks.
I have similar needs as yours, thus I tried to find a maximum of documentation and scientific results about mediums for long-term cold archival of digital data.
Results: I found a lot of documentation, but very few using independent scientific results, and in the end, no perfect solution emerged from those studies.
The first thing to clarify is what you are looking for (following your description):
Long-term archival: you don't just want to store backups of your OS, but you want to keep copies of your sensible, irreproducible data. Archiving is fundamentally different than a backup, as well explained here. A short definition of the difference: backups are for data that regularly get updated and thus need to be refreshed into backups, whereas archives are static data that you would likely write only once and just read from time to time. Archives are for intemporal data.
Cold storage: you want to avoid maintenance of your archived data as much as possible. This is a BIG constraint, as it means that the medium must use components and a writing methodology that stay stable for a very long time, without any manipulation from your part, and without requiring any connection to a computer or electrical supply.
To meet both criteria is impossible, thus I propose to prioritize cold storage by choosing mediums that maximize the data retention time without any manipulation, and then long-term archiving by choosing methods that should avoid losing data in the long run.
Cold storage mediums
We already defined above what a good cold storage medium should be: it should retain data for a long time without any manipulation required (that's why it's called "cold": you can just store it in a closet and you do not need to plug it into a computer to maintain data).
Hard Drives (HDDs) are known to have an average life span between 3 to 8 years: they do not just degrade over time, they are guaranteed to eventually die. The following curves show this tendency for all HDDs to die at a staggering rate:
Curves showing the evolution of HDD failure rate depending on the error type:
Curve showing the evolution of HDD failure rate by merging all error types:
From a post on Apple community by PlotinusVeritas.
You can see that there are mainly 3 types of HDDs relatively to their failure: the rapidly dying ones (eg: manufacturing error, bad quality HDDs, head failure, etc.), the constant dying rate ones (good manufacturing, they die for various "normal" reasons, this is the case for most HDDs), and finally the robust ones that live a bit longer than most of HDDs but they eventually die too not too long after the "normal ones" (eg: lucky HDDs, not-too-much used, ideal environmental conditions, etc..). Thus, you are guaranteed that your HDD will die, even if it's robust and if you are lucky, simply because this magnetic technology is not made to guarantee long term retention of data.
In addition, HDDs are known to demagnetize over time if not used (including SSD). Thus, you cannot just store data on a hard disk, store it in a closet and think that it will retain data without any eletrical connection. Thus, HDDs are clearly not a good fit for cold storage. This also rules out magnetic tapes (even if they are more reliable than HDD, they are still not a good fit for cold storage for the same reasons, as their primary focus is for backups, not long-term archives).
CompactFlash and SecureDigital (SD) cards are known to be quite sturdy and robust, able to survive catastrophic conditions.
The memory cards in most cameras are virtually indestructible, found Digital Camera Shopper magazine. Five memory card formats survived being boiled, trampled, washed and dunked in coffee or cola.
However, as any other magnetic based medium, it relies on an eletrical field to retain the data, and thus if the card runs out of juice, data may get totally lost. Thus, it may be not a good fit for cold storage (as you would need to regularly plug the card, or rewrite on the card, to refresh the electrical field), but it can be a good medium for backups and short-term archival.
Optical mediums: Another possibility is to use optical mediums, like CD, DVD or BluRay (BD). Like any technology, new iterations not only offer bigger density (storage room), but also error correction along other features. The first debate about DVD reliability was between DVD-R and DVD+R, and even if DVD-R are still common nowadays, DVD+R are recognized to be more reliable and precise.
DVD have since seen emerged archival grade discs, specifically made for cold storage, and which claim that they can withstand a minimum of about 20 years without any maintenance:
Verbatim Gold Archival DVD-R [...] has been rated as the most reliable DVD-R in a thorough long-term stress test by the well regarded German c't magazine (c't 16/2008, pages 116-123) [...] achieving a minimum durability of 18 years and an average durability of 32 to 127 years (at 25C, 50% humidity). No other disc came anywhere close to these values, the second best DVD-R had a minimum durability of only 5 years.
Furthermore, some companies even specialized in very long term DVD archival and extensively market them, like the M-Disc from Millenniata or the DataTresorDisc, affirming that they can retain data for over 1000 years, and verified by some (non-independent) studies (from 2009) among less-scientific others.
This all seems very promising! Unluckily, there's not enough independent scientific studies to confirm these claims, and the few ones available are not so enthusiastic:
Humidity (80% RH) and temperature (80°C) accelerated ageing on several DVDs over 2000 hours (about 83 days) of test with regular checking of readability of data:
Translated from the french institution for digital data archival (Archives de France), study from 2012.
The first graph show DVD with a slow degradation evolution. The second one DVD with rapid degradation curves. And the third one is for special "very long-term" DVDs like M-Disc and DataTresorDisc. As we can see, their performance does not quite fit the claims, being lower or on par with standard, non archival grade DVDs!
However, inorganic optical discs such as M-Disc and DataTresorDisc get one advantage: they are quite insensible to light degradation:
Accelerated ageing using light (750 W/m²) during 240 hours:
These are great results, but an archival grade DVD such as the Verbatim Gold Archival also achieves the same performance, and furthermore, light is the most controllable parameter for an object: it's quite easy to put DVD in a closed box or closet, and thus removing any possible impact of light whatsoever. It would be much more useful to get a DVD that is very resilient to temperature and humidity than light.
This same research team also studied the BluRay market to see if there would be any brand with a good medium for long term cold storage. Here's their finding:
Humidity and temperature test, under the same parameters as for DVDs:
Light test, under the same parameters:
Translated from this study from Archives de France, 2012.
Two summaries of all findings (in french) here and here.
In fine, the best BluRay disc (from Panasonic) performed similarly to the best archival grade DVD in humidity+temperature test, while being virtually insensible to light! And this BluRay disc isn't even archival grade. Furthermore, BluRay discs use an enhanced error correcting code than DVDs (themselves using an enhanced version relatively to CDs), which further minimizes the risks of losing data. Thus, it seems that some BluRay discs may be a very good choice for cold storage.
And indeed, some companies are starting to work on archival grade, high density storage BluRay discs like Panasonic and Sony, announcing that they will be able to offer 300 GB to 1TB of storage with an average life span of 50 years. Also, big companies are turning themselves towards optical mediums for cold storage (because it consumes a lot less resources since you can cold store them without any electrical supply), such as Facebook which developped a robotic system to use Blu-ray discs as "cold storage" for data their system rarely access.
Long Now archival initiative: There are other interesting leads such as the Rosetta Disc project by the Long Now museum, which is a project to write microscopically scaled pages of the Genesis in every languages on earth the Genesis got translated to. This is a great project, which is the first to offer a medium that allows to store 50 MB for really very long term cold storage (since it's written in carbon), and with future-proof access since you only need a magnifier to access the data (no weird format specifications nor technological hassle to handle such as the violet beam of the BluRay, just need a magnifier!). However, these are still manually made and thus estimated to cost about $20K, which is a bit too much for a personal archival scheme I guess.
Internet-based solutions: Yet another medium to cold store your data is over the net. However, cloud backup solutions are not a good fit, for the primary concern than the cloudhosting companies may not live as long as you would like to keep your data. An alternative is to rent your own private server online, and if possible, choose one with automatic mirroring/backup of your data in case of hardware failure on their side (a few ones even guarantee you against data lost in their contracts, but of course it's more expensive). This is a great solution, first because you still own your data, and secondly because you won't have to manage the hardware's failures, this is the responsibility of your host. And if one day your host goes out of business, you can still get your data back (choose a serious host so that they don't shutdown over the night but notify you beforehand, maybe you can ask to put that onto the contract), and rehost elsewhere.
If you don't want to hassle of setting up your own private online server, and if you can afford it, Amazon offers a new data archiving service, called Glacier. The purpose is exactly to cold store your data for the long-term: thus, it costs a lot to store data on a Glacier, but it costs even more to get back this data, as this service is made to store data out of reach, not to keep data that you want to often access. This means that this service quotes prices for writing data, but also for reading them. This service has a huge cost, but it may be a good deal for some of your most sensible data (ie: if you have a few text files or images that are VERY sensible, since this kind of data is usually of small size, it won't cost you very much to store in a Glacier).
Shortcomings of cold storage: However, there is a big flaw in any cold storage medium: there's no integrity checking, because cold storage mediums CANNOT automatically check the integrity of the data (they can merely implement error correcting schemes to "heal" a bit of the damage after corruption happened, but it cannot be prevented nor automatically managed!) because, contrariwise to a computer, there's no processing unit to compute/journalize/check and correct the filesystem. Whereas with a computer and multiple storage units, you could automatically check the integrity of your archives and automatically mirror onto another unit if necessary if some corruption happened in an data archive (as long as you have multiple copies of the same archive).
Even with the best currently available technologies, digital data can only be cold stored for a few decades (about 20 years). Thus, in the long run, you cannot just rely on cold storage: you need to setup a methodology for your data archiving process to ensure that your data can be retrieved in the future (even with technological changes), and that you minimize the risks of losing your data.
There's no foolproof rules here, but there are some well accepted advices:
Redundancy principle: this is not an advice, this is based on information theory. To keep data, you need to duplicate this data. Error codes are exactly an automatic application of the redundancy principle. However, you also need to ensure that your data is redundant: multiple copies of the same data on different discs, multiple copies on different mediums (so that if one medium fails because of intrinsic problems, there's little chances that the others on different mediums would also fail at the same time), etc. On this topic, a software called DVD Disaster offers to add error correction codes (in addition of those already implemented in storage mediums) to your data to ensure redundancy. I didn't try it (yet), but the idea of allowing the user to choose the percentage of error-correction is certainly enticing and should be promoted, as error-correction codes are VERY efficient (potentially a lot more than just duplicating your data on the same disc, see for example convolution error codes). For example, using TurboCodes (a recursive convolutional error code, used for 3G and 4G), you can expect to correct a lot more using the same amount of data (see redundancy rate and F merit rate, a very good introductory book being this one in French, or this one in english, both by the TurboCodes author).
Verify the integrity of your files before (re-)copying them: Hash your files, and check them before and after making copies/archives (because your files copies can get silently corrupted, and if you then copy the copies that have been tampered, you will end up with totally corrupted files). This point is very important, because cold storage mediums CANNOT automatically check the integrity of the data (they can merely implement error correcting schemes to "heal" a bit of the damage after corruption happened, but it cannot be prevented nor automatically managed!) because, contrariwise to a computer, there's no processing unit to compute/journalize/check and correct the filesystem. There's a software called CDCheck specifically made for this purpose, but you can just use any GNU hashing software, they are easy to script to batch process your whole data collection.
Store your archives mediums on different locations (and not only in your house!) to avoid for real life catastrophic events like flood or fire.
Store in specific containers with controlled environmental parameters: for optical mediums, store away from light and in a water-tight box to avoid humidity. For hard drives and sd cards, store in anti-magnetic sleeves to avoid residual electricity to tamper the drive.
Use good hardwares and check them beforehand (eg: when you buy a SD card, test the whole card with softwares such as HDD Scan to check that everything is alright before writing your data). This is particularly important for optical drives, because their quality can drastically change the quality of your burnt discs, as demonstrated by the Archives de France study (a bad DVD burner will produce DVDs that will last a lot less).
Store alongside your data archives every softwares and specifications that are needed to read the data. Remember that specifications change rapidly, and thus in the future your data may not be readable anymore, even if you can access the file. Thus, you should prefer open source formats and softwares, and store the program's sourcecode along your data so that you can always adapt the program from sourcecode to launch from a new OS or computer.
Lots of other methods and approaches are available here, here and in various parts of the Internet.
You should use whatever technology you see fit and which you are the most confortable with. Also, ensure that the hardware you use is of good quality (ie: the quality of the DVD/BD burner impact as much as the quality of the blank DVD/BD you will use to store your data, as demonstrated by the Archives de France study).
Personally, I would (will) primarily use BluRay HTL discs or archival grade DVD discs stored in water-tight boxes and away from light. I will also maintain copies on SD cards and HDDs (mainly for data that changes over time, like working documents) that I will regularly burn on multiple BluRay discs. I would also store those discs in multiple locations: one in my own house, one at my relatives, and maybe one at a safe deposit box at the bank for really sensitive data.
More importantly, I would regularly checkup on the integrity of the data stored on those discs by checking the MD5 or SHA-1 hash I computed on the files before burning them to the disc. If you can checkup twice a year, I feel that would be the best, but if not, I think that using a combination of optical and magnetic mediums and multiple copies you can still safely check only every few years (like every 3 to 5 years) without having too much to worry about.
On a final note, I really do hope that more R&D will be put on this problem. This is a major issue for our current society, having more and more data digitalized, but without any guarantee that this mass of information will survive more than a few years. That's quite depressing, and I really do think that this issue should be put a lot more in the front, so that this becomes a marketing point for constructors and companies to make storage devices that can last for future generations.
Automating long-term cold store management?
Companies managing big volumes of data need to be able to automatically manage archives and errors, and automatically ensure their integrity (like for example Facebook with the automated BluRay based cold storage facility).
However, to my knowledge, there's nothing like that for home consumers. Indeed, one of the big hassle in long-term storage, is that even if you can use cold storage mediums, you still have to manually check the integrity regularly. Wouldn't it be great if it would be done automatically, and alert you if one of the data archives failed? Even more, wouldn't it be great if such a system could then automatically use other copies of the corrupted archived data to create a new copy (ie: burning on a new BluRay disc or any other medium of choice), thus ensuring that you always keep x copies of your archived data at any given time?
Unfortunately, such a system does not exists. But, we could easily imagine a simple script running on a minimal computer like a Raspberry Pi to be the processing unit of this system. The only remaining problem would be to make a mechanical system to automatically load/unload and seek through a physical library of optical discs. Or you could do that with magnetic tapes such as LTO4. Of course, you would still need to manually dispatch some of those copies in off-house sites to account for natural catastrophic events, but it would be quite foolproof for any other type of event, as long as you maintain your Raspberry Pi on electrical supply, and that you replace its components when they wear off (like the disc burner).