Approach as for the normal (South) route, then once past it's difficulties (getting lost in the forest, or too wet in the waterfall, or frustrated by the brush :-) ), you have two choices:
1) From the relatively flat valley above the waterfall, with Mount Redoubt looming on your right, cross Depot Creek somehow and hike up to camp on moraines beneath the glacier. Ascend the glacier to reach the ice apron you intend to climb.
2) This was our choice, and it worked well. Hike up to camp at Ouzel Lake. In the morning, hike and scramble steeply up the rocky shoulder west of the lake. Once on the crest of the shoulder, don't go higher than 6,300 feet, travelling west, staying below another steep shoulder that climbs southeast to the summit. Once past this second shoulder, ascend the glacier as crevasses allow to reach the objective ice apron.
The route was first climbed by Fred Beckey and John Rupley on July 23, 1971.
Study the ice apron above you and chose a route through the 1-3 major bergschrunds that may pepper it's lower half. Our strategy was to use these schrunds as belay locations. This worked well, as they were actually crevasses with easy entry and nice floors from the bottom. Then we'd traverse out of it to the left and continue up.
We stayed on snow the entire way up to a (not really visible from below) spectacular snow arete that tops the apron. We belayed most of the way, simulclimbing for a while in the middle and at the end. Snow conditions were good in the shade, occasionally unnerving in the sun (get up early).
Some have reported climbing rock to the left of the apron, but this didn't look wise to us, as it appeared steep and time-consuming.
Once on the snow arete, climb it to it's head 200 feet above, then make a belayed traverse on steep snow to the left in order to gain entry to another couloir. Actually, it's best to traverse left about 30 meters, then climb a pitch or two of easy rock straight up a shallow basin on the right of this couloir. At this point, you can easily downclimb 20 feet to get into the couloir at a secure point.
(The reason for the detour to rock is that the steep snow traverse is not likely protectable. We had heard a story of a near disaster making this traverse involving a slip and a lucky catch because the belayer knew his ice axe and picket belay was worthless.)
Once in this upper couloir, climb the right side, protecting with rock gear and slings until the angle relents somewhat, and you can kick steps to the top. There may be an enormous cornice to pass here, though our July ascent had no such trouble.
From a comfortable notch above this couloir, scramble rightward on loose ledges to eventually meet the South Route. You might want to belay a portion of this rightward traverse, we found some awkward low 5th class climbing here.
Head right uphill along this scramble route (a few cairns mark the way) through enjoyable gullies to a final short but steep scramble (possibly snow) below a cannonhole formation. Climb through it to emerge back on the north side of the mountain. The summit is about 100 feet above on the left - scramble or belay up to it on steeper exposed terrain (4th class).
To get down, retrace your route through the cannonhole, possibly making a rappel above it and just below it. Continue down to the south, trending left where appropriate to reach a broad snow gully heading due south. This gully steepens near the bottom, step carefully and watch out for holes with water beneath.
At the bottom of the gully turn left and uphill to gain a col leading to the Redoubt Glacier. Jump down to the relatively crevasse-free glacier and walk down, eventually reaching the rocky shoulder west of the lake that you remember from the morning. Go to camp and drink some nice glacial flour water as a reward!
I hate nothing more than hiking a long distance in full-shank heavy duty boots. But they are needed for the extensive steep snow and possible ice climbing on this route. Bring two ice tools, 3-4 ice screws, several pickets, 6 nuts, 3-4 smaller cams, and a few pitons. Don't forget the glacier gear like pulleys, prussiks and extra slings, because the Depot glacier requires snowbridge crossings.
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