The forecast for today, by both services, is for highs around 90F with mostly sunny to sunny skies. Thus, the issue does not have to do with weather forecasted for today.
Currently it is 72F at 10 am in Philip, SD with calm winds. However, the flow is generally out of the south throughout the region and will likely increase in Philip as the day progresses. Dewpoints are in the mid-50s to near 60 from Canada through SD.
Taking a quick look at the GFS model to get a general feel of the weather over today and tomorrow, the GFS keeps a southerly flow into the Dakotas through tomorrow mid-day. Near 18Z or 00Z a mid-lat cyclone will move to the east through southern Canada. This will bring a trailing cold front through North/South Dakota somewhere between those hours. This cold front will be the triggering mechanism for any thunderstorms tomorrow. It will also lead to cooler air moving into the region, possibly indicating why TWC and NWS have such differing high temperatures, as the timing could be difficult to pinpoint.
GFS model:
Today the 850 mb temps, under the southerly flow, will peak at 22C this afternoon, supportive of 30C/86F high temperatures, a little cooler than both TWC and NWS. Mixing looks to be minimal with only 4-6 mph winds predicted at the surface. The Philip area will be under NWesterly flow aloft at 200-700 mb, as an upper level ridge slides eastward. The crest of the ridge will move over the Dakotas around 12Z tomorrow as a 500 mb vort max moves through western MT and southern Canada. This vort max looks like it will traverse mostly north of South Dakota, leading to PVA mainly in southern Canada and ND near 18Z. The PVA looks to be lagging behind the surface boundary throughout the frontal passage, reducing the influence it will have on storm initiation. However, with the added convergence from the cold front, and dewpoints in the mid-50s, shower/t-storm development looks possible over ND into SD (and in Canada). I would put the highest risk of rainfall in mid-ND northward.
As for 850 mb temps tomorrow, they increase to 25C by 4 pm, or supportive of 33C/92F. The RAW GFS forecasts a high of 94F. This is much cooler than temperatures forecasted by the NWS. Little moisture is found at 700 mb, which leads to questioning about shower possibilities in the region. However, CAPE will increase to 500-1000 J/kg near 18Z, as the cold front traverses through Philip. CIN will also be high, 200-300 J/kg, no helicity, and LI of -3. In other words, there is a decent amount of instability, but with high CIN, any convection will be unlikely surface based with the LCL over 700 mb and the LFC at 600 mb! Basically, things look caped in the Philip area, and the GFS does not produce any rainfall for SD at all.
As for the NAM:
850 mb temps today: 23C, supportive of 88F. 850 mb temps tomorrow: 30C, supportive of 100F! Already we are seeing a major difference in the models. Add in dewpoints near 60F for Philip, rather than mid-50s for the GFS, and things could be very different tomorrow.
A few things are similar between the models. They both bring the ridge over the area tomorrow afternoon, with a 500 mb vort max traversing through MT/southern Canada into ND, missing SD. It is again lagging behind the cold front. However, a small bit of vorticity is shown over the Black Hills at 18Z, putting a little PVA right over the Wall/Philip area in the heat of the afternoon. Add in that the NAM isn't forecasting the frontal passage until 20Z, this gives the opportunity of storms a bit more possibility.
The RAW NAM is forecasting a high of 103F, which doesn't really scream severe weather. Rather, it screams CAP! Looking at the CAPE forecast by the NAM, it is much higher in the 1500-2000 J/kg range, with CIN dropping to near 30-50 J/kg from 20Z-21Z, just as the front passes but over 100 J/kg every other hour during the day. The LCL/LFC levels are above 700 mb, so elevated convection looks like the most likely possibility, if there is any. Helicity is still low, 0-100 m2/s2, indicating difficulty to have rotating updrafts. Actually, as the CIN decreases, Helicity values drop to 14 m2/s2, decreasing the rotation possibilities.
The 22-km WRF initiates convection in the center of SD/ND and only gives a quick pulse of convection, reducing certainties that severe weather looks likely. Actually, the greater chance of precipitation looks post-frontal as a secondary low develops in CO/WY and brings in shower/tstorm activity in the late evening into the morning hours (nocturnal MCS time!).
So what do I think about the severe weather?
The possibilities look low for the Philip area, but higher to the north in ND. The SPC places a 15% chance of severe weather tomorrow from Philip north to the Canadian border, east to the MN border. I think there will be a few severe storms tomorrow, but they will be short lived in the SD area. If the small vort max in the Black Hills, shown by the NAM, actually exists, there could be a chance of a storm in the Philip region as the front moves through, but it seems a bit fishy and not prudent to jump on such a small vort max. I will go with a 20% chance of storms from the front here in Wall/Philip.
As for the Temperatures:
The ETA MOS is forecasting low 90s today, 98F tomorrow, and the GFS MOS is much the same (low 90s/97F). Considering the large spread in 850 mb temperatures tomorrow, this forecast is very difficult. There are a few things that lead me to lean towards the higher end, the first being the very high 850 mb temps forecasted by the NAM, the second the agreement between the MOS values (and raw GFS of 94F), and the high levels of CIN tomorrow likely holding back storm initiation. RAW NAM has winds out of the south at 10 mph, enough for good mixing. However, the frontal passage is near 2-4pm, and if it does have any cloudiness with it (and the lowering 850 mb temps behind it), temperatures could have a difficult time at peaking at the 103F thought by the RAW NAM and its 850 mb temperatures.
Thus, 88F today (held back by 850 mb temps, not cloudiness) and 96F tomorrow. I think the area will heat up quickly in the morning and try to climb towards the 850 mb temp potential forecast by the NAM, but the frontal passage, and any cloudiness with it, will stop the climb around 2pm. By the time skies clear a bit again the 850 mb temps will be back down 5 C, only supportive of 94F. Lows tonight, under clear skies and 4-5 mph winds, should drop easily. Dewpoint temperatures forecast by the MOS are near 60F, with ETA/GFS MOS forecasting 62F/60F respectively. I don't have a problem with those temperatures, I'll go 61F.
My numbers: 88/61/96
NWS numbers: 90/64/97, then upped to 92/64/99 at 11 am
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