Cyclocross is hard, plain and simple. There are very few sports that require the same level of intensity from start to finish over the course of an hour as a cyclocross event, where you're trying to perfom at maximum output for the entire duration, combined with technique that requries a high level of skill and responding to unpredictiable scenarios, while still also thinking critically and making tactical decisions, too.
Some might argue that like cyclocross, a 40K time trial also lasts about an hour, and requires the maximum effort possible over that time. This is true, in terms of generally defining the effort as "as hard as you can go for an hour." What's different about cyclocross, on top of the fact that it's a cold, muddy, and slippery version of the 40K time trial, is that the power requirements are different. The way you spread that "maximum effort" out over the course of the hour varies dramatically from a standard time trial. If you were to look at a graph of power and heart rate for a flat 40K time trial, you'd see two very steady, even lines. And so your training for time trials would reflect just that; a lot of steady-state intervals of various lengths, consistent in terms of both heart rate and power.
When you look at a power and heart rate graph of a cyclocross race, however, what you see is strikingly different. The heart rate line will look similar to the 40K TT: pegged and steady for the entire hour. The power is where the difference lies. The maximum effort you produce for a cyclocross race is one of sharply varying power, showing the effect of varying terrain. 'Cross is a sport of transitions and speed changes. Full on the brakes here for this corner, full acceleration out of the corner. Foot out and sliding across an off-camber hill here, sprinting up over the other side there. Coasting a bit before the hurdles, followed by a max effort run, remount, and re-acceleration immediately after. Whereas average power for a 40K TT will see you actually riding at that average power during the event, power in a 'cross race will consist of continual large fluctuations above and below functional threshold power, even though both efforts will keep you at a heart rate response at threshold for the duration of the event. This is the key difference, and in this way cyclocross resembles a full-gas one-hour criterium more than it does a 40K time trial.
What's different, then, in interval training for cyclocross, compared to what you might do for the road or mountain bike season? First and foremost, the base period, if you're focused on 'cross, is the same. You should be maximing the hours you have available and build the biggest workload of work below threshold you can in June, July and perhaps also August, depending on when you want to be at your best, in order to draw from that investment throughout the season. Of course, many people are struggling to get in the time to be fit for anything more than 1 hour race in the first place, summer or fall, so I often the volume of training for 'cross and road is the same. But you have the benefit of longer days and better weather in the summer, so it turns out to be much easier to do a big summer base for 'cross than it is to do a winter base for the road.
Just as you would afer a winter base for the road season, once that base is complete and you're withing a month of either the start of the season, or your first important races, you want to focus on higher intensity, supra-threshold interval work. Base is still important to 'cross, because you need a certain level of form to be able to recover from the stress of your interval training and racing, but once the racing starts, endurance in and of itself is not a priority. But when you plan your interval work for 'cross, you want to think in the same terms as you do in the summer, and define your work in categories of intensity, duration, frequency, and terrain or mode of work. I'll outline all the options in those parameters here.
Sprints
If you think about 'cross in terms of constantly varying power outputs at a steady threshold heart rate, then try to think about what racing situation you're in when you make those efforts. When you're making maximal efforts that are under 15 seconds in a 'cross race, you'll find the things you're normally doing are short run-ups, sprinting out of corners or hurdles, or sprinting off the start line. So those are exactly the activities you should work on in your sprint workouts. Keep the efforts between 8-15 seconds, give them 100% effort with 2-5 minutes of recovery between each, and try to reproduce your race situation so you can boil things down and combine technique work with physiological training. Start practice is my favorite way to combine technique training with physiological training. 3-15 sprints is the range of repeats to do.
Anaerobic Work Capacity
30 second to 2-minute long efforts over threshold are what make up much of the hour in a 'cross race. It's not that you spend a continual hour over threshold, it's that you spend 1 minute here, followed by 10 seconds of coasting, and another 30 seconds there, followed by a minute of steady riding just below threshold. The efforts are scattered throughout the race. You want to separate the 1-minute, anaerobic work capacity intervals out from your other training, and focus on them in specific workouts. These efforts should be done all out, unpaced, starting with a sprint and then hanging on for dear life for the remainder of the minute, with 5-10 minutes of full recovery between each, and a range of 2-6 repeats. Longer 'cross starts are an excellent mode for these efforts, as well as riding across any kind of challenging stretch of terrain.
VO2max
The 5-minute, VO2max focused intervals are probably the most important for 'cross, and feel most like the effort you're making during the race. These intervals work well when you can find a short 'cross course that you can do a lap on and a partial lap or paved recovery section off. This is where you can again combine training at high intensity with skill work, practicing your technique and line choices while at high speeds and under pressure. It's also here that you can really work on speed changes while being just over your limit. If a course is too technical, though, you won't be able to make the proper effort, so don't limit yourself by including too many turns. 5 minutes on, partial recovery of 2.5 minutes off, evenly paced, with 2-8 repeats as the range. The effort should feel like the first lap of a race.
Threshold
Middle makes up most of the "glue" of a 'cross race, and is that 12-20 minute long effort just at or below threshold when you're holding your spot in a group, or riding hard between sections trying to maintain your effort. In training, this is where you can work on varying power levels but with a consistent overal perceived exertion or heart rate response. Again, on a 'cross course, keep the overall effort steady, but let the power change based on the terrain. Sprint back up to speed after every corner and re-accelerate after every dismount, trying to get back up to your cruising speed where you know you can settle down again at the power you would hold if the effort stayed steady. Another ideal way to train in this zone is to motorpace. It may sound strange to motorpace for cyclocross, but motorpacing requires the same type of varying power effort at a high, steady heart rate as cyclocross and even criteriums, and can be effective training when your favorite 'cross course is under a foot of snow, but the roads are clear. Threshold efforts should be done as 15-20 minute efforts with 5-10 minutes off, for a range of 15-90 minutes of work total. 2 x 20s are a standard workout for most athletes at this point, and enough. Getting to the point where you can finish the volume of threshold interval work in training that matches your race duration let's you know you're ready for the next phase, and to start the season.
Tempo
You'll almost never be at tempo in a 'cross race unless you're having a bad day or you go out too hard and blow up, which obviously happens. Tempo is that steady, uncomfortable effort you might do sitting in in a road race or criterium, and you can hold for 30-60 or more minutes at a time. It's still important for 'cross though because it helps build your overall aerobic capacity and efficiency in such a way as to allow you to handle the higher intensity work to come and still recover, but also contributes to raising your FTP, too. You need to be able to have the capacity to warm-up, pre-ride the course, race, and cool down. So in your workouts, light can serve as your warm-up effort before your higher intensity, as well as the bulk of the intensity you'll do on your longer road ride. This should consist of 1-2 hours of total work in 30-60 minute blocks, and can be most of your ride if you're pressed for time, or as little as half your ride if you've got more time to work with. Some riders will get out and smash an hour of tempo and finish at their front steps, whereas a pro might do 3 x 60 over the course of a 6-hour ride in their base period.
Because 'cross is such a high-intensity, full body sport, one of the biggest things you need to focus on is recovery. You may find that after a weekend of racing you won't be ready to train again until Wednesday or even later, especially if you've done two races. One day of recovery for each day of racing is a great guide to follow once the season starts. By focusing on full recovery between racing and training, and 'cross-specific intervals when you do head out to train, you should find your performances on the weekend improve accordingly. Much of the work for 'cross has to be done in the months before the season starts, since racing can often leave you too tired to train mid-week. When you do need to rebuild your form mid-season, a weekend off from racing is almost mandatory, in order to get the rest and space to actually be recovered enough to do the re-investment training required. Hopefully these interval descriptions can serve as a guide for what to work on, when.