During unreliable air speed whilst the crew held the wings level using constant left roll input, but with a mistaken light back pressure, it trimmed the aircraft fully nose up in response - without them realising. That's bad.

The thrust levers were positioned in the TO/GA detent and the PF maintained nose-up inputs.

The PF made an input on the sidestick to the left and nose-up stops, which lasted about 30 seconds.

not sure where "light back pressure" comes from?

History
History
One of the more interesting (to me) on-line documents relating to the history of recommendations concerning the use (or non-use) of trim during recovery from upsets in transport aircraft is a talk given by Captain William Wainwright, Chief test pilot of Airbus.

The full text is available from at least two sources (one being the NTSB).
http://www.ntsb.gov/Events/2001/AA58...its/240005.pdf
http://www.skybrary.aero/bookshelf/books/435.pdf

Here are some extracts. The omission of text in these extracts is indicated by “………”.

--------- Start of quote extracts -----------
AIRPLANE UPSET RECOVERY TRAINING AID,
By Captain William Wainwright, Airbus Industrie.

INTRODUCTION
The idea for a joint industry working group to produce an Airplane Upset Recovery Training Aid was first proposed by ATA in June 1996. ........ The end result of 2 years work is a training package including a video and a CD-ROM, giving an airplane upset recovery training aid. This package is on free issue to all of you, to use or not to use as you wish. ………..The content of the package is not my subject today, but there are a few issues of general interest which I gained from my experience as a member of the working group which I would like to talk about.

2. THE BEGINNING
…… Right from the beginning there was a conflict between the technical advice given by the manufacturers' training pilots and that expressed by those of the principal airlines already practicing upset training. They naturally considered themselves to be the experts on this subject, based on the many .hours of training that they had already conducted on a large number of pilots in their simulators. At the beginning of 1997, the Flight Test Departments were asked to come in to support their training pilots. From then on, the chief test pilots of the 3 major manufacturers became members of the working group; XXX of Boeing, YYY of McDonnell-Douglas (now Boeing - Douglas Products), and myself. But the conflict over the different opinions on aircraft handling and recovery techniques continued for a long time until we finally achieved agreement at the last meeting in January 1998. The reasons for these differences of opinion are the subject of my talk today.

3. THE DIFFERENCES
The differences of opinion were mainly concentrated in the following areas:
(a) Procedures versus general advice.
(b) Ease of training versus failure cases.
(c) Stalling.
(d) Use of rudder.
(e) Use of simulators.

It is worth saying that there was never any difference of opinion between the three test pilots on the group. Although we come from different backgrounds and have worked in different organizations with different work cultures, we always agreed on our technical advice.

4. PROCEDURES VERSUS GENERAL ADVICE
The airlines wanted simplified procedures which were common to all aircraft in their fleets and which were easy to teach and easily reproducible. This is understandable because you are all interested in having a standard product at the end of your training programmes. And this is what they already had with the Airplane Upset Recovery Training that they were already doing. For the training managers from American Airlines, Delta, and United, the only thing necessary was to give an overall industry approval to their existing programmes; they already worked, because the many pilots that had undergone training all came out of it with the same standardized reactions to the standard upsets. For them, this was the necessary proof that their training programme worked.

Where we differed was in our conviction that there was no such thing as a standard upset and our reluctance to endorse simplified procedures for recovery from an upset. We wanted a general knowledge based approach, as opposed to a rule based one. For this, after proposing some initial actions, we talk about “additional techniqlies which may be tried”. This obviously is more difficult to teach. ...........

5. EASE OF TRAINING VERSUS FAILURE CASES
The training that was already being done considered upsets as being due to momentary inattention with a fully serviceable aircraft that was in trim when it was upset. We would like to consider other cases that involve failures of control systems or human errors leaving the aircraft with insufficient control authority for easy recovery.

This of course complicates the situation, because recovering an aircraft which is in trim, possessing full control authority and normal control forces, is not the same as rocovering an aircraft with limited control available or with unusual control forces. Thus, for us, an aircraft that is out-of-trim, for whatever reason, human or mechanical failure, should be re-trimmed. Whereas the airline instructors were against the use of trim because of concerns over the possibility of a pilot overtrimming and of trim runaways which are particularly likely on some older aircraft types which are still in their fleets. We spent a lot of time discussing the use of elevator trim, and we never reached agreement. All the major US airlines were adamant on their policy to recover first using “primary controls” which excluded any reference to trimming. Again, a compromise was necessary. What we have done is to talk about using trim if a sustained column force is required to obtain the desired response whilst mentioning that care must be used to avoid using too much trim. And, the use of trim is not mentioned in the simplified lists of actions to be taken.

6. STALLING
Another aspect that was 'being ignored in the existing training was the stall. By this I mean the difference between being fully stalled and the approach to the stall. In training, you do an approach to the stall with a recovery from stick shaker, which is often done by applying full thrust and maintaining existing pitch attitude in order to recover with minimum loss of height. Height cannot be maintained if an aircraft is actually stalled and should be of secondary importance. .......

There is a world of difference between being just before, or even just at, the stall, and going dynamically well into it. The training being given in the airlines at the time to recover from excessive nose-up pitch attitudes emphasised rolling rapidly towards 90" of bank. This is fun to do, and it was not surprising to find that most of the instructors doing the training were ex-fighter pilots who had spent a lot of time performing such manoeuvres in another life. The training was being done in the same way, with an aircraft starting in trim with a lot of energy and recovering while it still had some. However, the technique being taught only works if the aircraft is not stalled. ……..
If the airplane is stalled, it is imperative to first recover from the stalled condition before initiating the upset recovery technique. Do not confuse an approach to stall and a full stall. An approach to stall is controlled flight. An airplane that is stalled is out of control and must be recovered.
A stall is characterised by any, or a combination of the following:
--- Buffeting, which could be heavy at times.
--- A lack of pitch authority.
--- A lack of roll control.
--- Inability to arrest descent rate.
To recover from a stall, the angle of attack must be reduced below the stalling angle. Apply nose down pitch control and maintain it until stall recovery. Under certain conditions with under-wing mounted engines, it may be necessary to reduce thrust to prevent !he angle of attack from continuing to increase. Remember, in an upset situation. If the airplane is stalled, It is first necessary to recover from the stall before initiating upset recovery techniques. This is something that we are well aware of in testing, but it was either being totally ignored, or misunderstood. I consider the inclusion of this note to be one of our most important contributions.

8. USE OF SIMULATORS
We manufacturers were very concerned over the types of manoeuvres being flown in simulators and the conclusions that were being drawn from them. Simulators, like any computer system, are only as good as the data that goes into them. That means the data package that is given to the simulator manufacturer. And we test pilots do not deliberately lose control of our aircraft just to get data for the simulator. …………..

The complete data package includes a part that is drawn from actual flight tests, a part that uses wind tunnel data, and the rest which is pure extrapolation. If should be obvious that conclusions about aircraft behaviour can only be drawn from the parts of the flight envelope that are based on hard data. This in fact means being not far from the centre of the flight envelope; the part that is used in normal service. It does not cover the edges of the envelope. I should also add that most of the data actually collected in flight is from quasi-static manoeuvres. Thus, dynamic manoeuvring is not very well represented. …………

In other words, you have reasonable cover up to quite high sideslips and quite high AOAs, but not at the same time. Furthermore, the matching between aircraft stalling tests and the simulator concentrates mainly on the longitudinal axis. This means that the simulator model is able to correctly reproduce the stalling speeds and the pitching behaviour, but fidelity is not ensured for rolling efficiency (based on a sirrpfified model of wind tunnel data) or for possible asymmetric stalling of Ihe wings. ......

In fact, this is a perfectly adequate coverage to conduct all normal training needs. But it is insufficient to evaluate recovery techniques from loss of control incidents. Whereas, the training managers were all in the habit of demonstrating the handling characteristics beyond the stall; often telling their trainees that the rudder is far more effective than aileron and induces less drag and has no vices In short, they were developing handling techniques from simulators that were outside their guaranteed domain. Simulators can be used for upset training, but the training should be confined to the normal flight envelope; For example, training should stop at the stall warning. They are "virtual" aircraft and they should not be used to develop techniques at the edges of the flight envelope. This is work for test pilots and flight test engineers using their knowledge gained from flight testing the "real" aircraft.
--------- End of quote extracts -----------

"At 2 h 10 min 16, the PNF said "so, we’ve lost the speeds" then "alternate law ...
The airplane’s pitch attitude increased progressively beyond 10 degrees and the plane started to climb. The PF made nose-down control inputs and alternately left and right roll inputs. The vertical speed, which had reached 7,000 ft/min, dropped to 700 ft/min and the roll varied between 12 degrees right and 10 degrees left."

He must have made some unnoticed back pressure input to climb.

Did it? How do we know, if we are looking at invalid speed indications?

At 2 h 10 min 16, the PNF said "so, we’ve lost the speeds" then "alternate law ...
The airplane’s pitch attitude increased progressively beyond 10 degrees and the plane started to climb. The PF made nose-down control inputs and alternately left and right roll inputs. The vertical speed, which had reached 7,000 ft/min, dropped to 700 ft/min and the roll varied between 12 degrees right and 10 degrees left.

Right from the beginning there was a conflict between the technical advice given by the manufacturers' training pilots and that expressed by those of the principal airlines already practicing upset training.

Absolutely agree. What happening outside the airframe could give that sort of energy and would appear by stick position, to be countered by the aircraft?

From 2 h 10 min 05, the autopilot then auto-thrust disengaged and the PF said "I have the controls". The airplane began to roll to the right and the PF made a left nose-up input. The stall warning sounded twice in a row. The recorded parameters show a sharp fall from about 275 kt to 60 kt in the speed displayed on the left primary flight display (PFD), then a few moments later in the speed displayed on the integrated standby instrument system (ISIS).
At 2 h 10 min 16, the PNF said "so, we’ve lost the speeds" then "alternate law [...]".
The airplane’s pitch attitude increased progressively beyond 10 degrees and the plane started to climb. The PF made nose-down control inputs and alternately left and right roll inputs. The vertical speed, which had reached 7,000 ft/min, dropped to 700 ft/min and the roll varied between 12 degrees right and 10 degrees left. The speed displayed on the left side increased sharply to 215 kt (Mach 0.68). The airplane was then at an altitude of about 37,500 ft and the recorded angle of attack was around 4 degrees.

I doubt that an object weighing hundreds of tonnes, moving at great speed under its own power and 10km in the air and designed to be in that environment, would end up in a simple trig equation, where vertical equaled horizontal. But it is one possibility I suppose.