What I've done is look at the forecasts and compared them to
each other. I haven't correlated whether the weather they
forecast actually happened, just how often the forecasts changed
(since a 5 day forecast that changes the very next day can't
be relied on, so isn't any use).

As the weather got more changeable after the summer, so the
accuracy of the forecasts dropped. Compared with August's 50%
likelihood of the next-day forecast being accurate, Spetember's
40% (i.e. it missed the mark on 3 more days) is disappointing.

The basic problem of having too many categories is even more
pronounced this time, as when I reclassified the 9 types of
weather in Septemer's forecast down to just the basics:
sun, cloud, rain the chances of being correct next day rise
to 77% and the forecast for +4 days goes from a lower than
random chance to a usable 11 days out of 30

forecast forecast on: times num of days
-- date -- on day D-1 D-2 D-3 D-4 correct changes ahead
Wed 1 Sep S S S S S 4 0 4
Thu 2 Sep S* SI SI SI SI 0 1 0 !
Fri 3 Sep SI S WC SI SI 2 3 0
Sat 4 Sep S SI S SI WC 1 4 0
Sun 5 Sep LRS SI SI S SI 0 3 0 !
Mon 6 Sep HR HR LRS SI SI 1 2 1
Tue 7 Sep HRS HRS HRS HR SI 2 2 2
Wed 8 Sep D LR LRS HRS HRS 0 3 0 !
Thu 9 Sep SI S SI SI HRS 2 3 0
Fri 10 Sep GC GC WC SI LR 1 3 1
Sat 11 Sep SI LR SI LR HR 1 4 0
Sun 12 Sep S SI SI S S 2 2 0
Mon 13 Sep SI SI SI SI S 3 1 3
Tue 14 Sep LR LR LR HR LR 3 2 2
Wed 15 Sep SI S S SI SI 2 2 0
Wed 15 Sep SI* S S SI SI 2 2 0
Fri 17 Sep S GC WC SI S 1 4 0
Sat 18 Sep SI SI SI HR SI 3 2 2
Sun 19 Sep SI* LR LR S HR 0 3 0 !
Mon 20 Sep SI* SI SI SI S 3 1 3
Tue 21 Sep SI* SI S LR S 1 3 1
Wed 22 Sep S S S S LRS 3 1 3
Thu 23 Sep HRS HRS HRS LRS LRS 2 1 2
Fri 24 Sep HRS* HRS LR HRS S 2 3 1
Sat 25 Sep S SI LRS SI GC 0 4 0 !
Sun 26 Sep SI GC SI LRS GC 1 4 0
Mon 27 Sep SI* HRS GC GC LRS 0 3 0 !
Tue 28 Sep GC SI SI WC SI 0 3 0 !
Wed 29 Sep LR HR HR LR GC 1 3 0
Thu 30 Sep SI S SI SI S 2 3 0

For last 30 days: avg 2.50 different forecasts per day
On average forecasted 0.83 days ahead
Correct 4 days ahead: 1 times
Correct 3 days ahead: 4 times
Correct 2 days ahead: 8 times
Correct 1 day ahead: 12 times (40.0%)
Number of times the weather was same as yesterday(*): 7 times (23.3%)
Number of days every forecast was wrong(!): 7 times (23.3%)

Key:
D: Drizzle 1 occurrences, predicted 0 times under-forecast
GC: Grey Cloud 2 occurrences, predicted 8 times about right
HR: Heavy Rain 1 occurrences, predicted 8 times over-forecast
HRS: Heavy Rain Shower 3 occurrences, predicted 10 times about right
LR: Light Rain 2 occurrences, predicted 12 times over-forecast
LRS: Light Rain Shower 1 occurrences, predicted 8 times over-forecast
S: Sunny 7 occurrences, predicted 26 times about right
SI: Sunny Intervals 13 occurrences, predicted 43 times about right
WC: White Cloud 0 occurrences, predicted 5 times over-forecast