Answer: The inch a week is a rule of thumb, just a general guide. If the weather is hot and/or dry and/or windy or if the soil is especially well drained (as it tends to be in raised beds) or you are growing plants that require an evenly moist soil, then you may need to water more often during a dry spell or drought. And, each watering must be thorough and deep -- an inch deep is nowhere near enough.
The best way to know if you need to water is to dig into the soil. If it is still damp, do not water yet. If it is dry then you need to water. When you water, apply it slowly and thoroughly so it soaks down to where the deeper roots are. After watering, wait a few hours and then dig down to see how far your water went. In this case, it sounds like you need to water much more generously -- meaning apply more each time you water -- so the soil is thoroughly moistened and the plants are fully hydrated after a watering. The time between waterings will depend on the above factors.
Keep in mind that an osciallating sprinkler usually has a mixed watering pattern with some areas receiving more than others, sometimes at a dramatic difference. (To really test it you would need to set out a pretty large number of tuna cans or similar uniform containers over the entire area you are watering to get a good sampling and see what the pattern is.) Sprinklers lose a good amount of the water to evaporation, too. The most efficient method of watering is a drip system where the water is applied to the roots of the plants.
In a raised bed situation the soil volume is relatively small and exposed to air at the perimeter(like in a container) and naturally dries out fairly fast as a result. Using an organic mulch about two to three inches thick will help keep the soil more evenly moist. And, it breaks down over time to add organic matter to the soil.
The type of soil in your raised beds is also very important in terms of watering. Since this is an intensive growing method, you really need to keep adding organic matter such as compost to the soil on an ongoing basis -- it has to be replenished often because it breaks down over time. The organic matter will help the soil to hold both air and water better.
As far as a fall planting, you can do spinach, lettuces and other greens along with peas and beets but wait another week or two and hope there is a break in the weather. It is a bit late for brassicas unless you can find good sized transplants. Look for quick maturing varieties, too.
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