KMDT vs KCXY — Polar ↔ Cartesian coordinate systems
Petal length = frequency of observations with wind arriving from that direction. Petal color = average wind speed for that sector. White arrow = mean resultant vector, pointing toward the direction wind is coming from.
Wind direction is circular — 359° and 1° are 2° apart, not 358°. You cannot average directions using regular arithmetic. The solution: decompose into u (east–west) and v (north–south) components, do math in Cartesian space, then convert back.
Why sin for u? Met directions are where wind comes FROM, measured clockwise from North. sin(0°)=0 gives no east component when wind is from N. sin(90°)=1 gives full east component when wind is from E. ✓
atan2(u, v) not atan2(v, u) — because our reference axis is North (v), not East (u). This is the key difference from standard math convention.
You were right to think of arctan. After computing mean u and mean v across all observations, you have a resultant vector expressed as (u,v) components. To express that as a compass bearing, you need the angle — that's atan2(u, v).
The reason atan2 (two-argument) rather than atan (one-argument) is that dividing u/v loses the sign information needed to distinguish NE from SW. atan2 preserves it by taking both components separately. It's the standard tool for any "vector angle from components" problem.
Step 1: Are distributions comparable? Both ~40–46k seasonal obs, same 2005–2026 window — yes. Step 2: Can I use scalar means? No — direction is circular. Step 3: Decompose to u/v, compute mean components, then: (a) mean vector for net drift character, (b) binned frequency profiles for modal structure, (c) look for bimodality (NW+SE) vs unimodality (E or W). The big question: is the difference meteorological or orographic?
The most diagnostic result across all seasons: CXY consistently shows high east-wind frequency that MDT almost never sees. Both stations experience the same synoptic regimes. The difference is purely mechanical: the Susquehanna River cuts through Blue Mountain at CXY's location, creating a topographic funnel that accelerates and aligns flow along the E–W axis.
This is textbook gap-flow physics. Any wind homogenization work comparing these two stations must account for this structural difference — it's not a data artifact.
119,853 matched hour pairs (2005–2026, all seasons). For each hour both stations reported, we computed the vector difference: subtract CXY's (u,v) from MDT's (u,v) and take the magnitude. This is not a speed difference — it captures disagreement in both direction and speed simultaneously. One erroneous MDT observation (108 mph on 2017-06-27, almost certainly an anemometer fault) was removed, leaving 119,852 clean pairs.
NW post-frontal flow produces the largest station differences — MDT accelerates down the Cumberland Valley while CXY sits in the river-bend bowl with a weaker, more variable response. Counterintuitively, purely easterly flow (CAD events) produces the smallest differences — both stations experience east wind, but CXY amplifies it while MDT is partially blocked.
The peak divergence at 15–19Z (roughly 11AM–3PM Eastern) is the afternoon convective mixing signal. During peak heating, the planetary boundary layer grows and the surface wind at both stations couples more strongly to synoptic flow — but MDT, sitting in the open valley, responds more vigorously than CXY in its sheltered river-bend position. The result is maximum station disagreement during afternoon hours. The pre-dawn minimum (22–01Z, ~6PM–9PM local) is when both stations settle into similar light-wind nocturnal regimes.
This occurred 1,138 times (roughly 1% of all matched hours). It is the direct observational signature of the orographic hypothesis: post-frontal NW flow reaching MDT through the Cumberland Valley while the Susquehanna corridor funnels residual easterly flow to CXY. Mean vector difference during these hours: 5.79 mph — 27% above the overall mean.
| Date/Time (UTC) | MDT (FROM) | CXY (FROM) | Vector Diff | Note |
|---|
Divergence is remarkably flat month-to-month (range: 4.32–4.78 mph), confirming the orographic effect is structural and season-independent. The slight April peak aligns with the most active frontal passage period. September minimum reflects the quietest synoptic period of the year.
These use the complete IEM windrose tables: MDT back to Dec 1972, CXY back to Jan 1970 — far longer than the 2005–2026 paired dataset. The monthly mean vectors reveal how the terrain signature evolves through the calendar year, and September's 50° directional gap between the two stations is the most striking single finding.
September stands out: MDT FROM 318° vs CXY FROM 268° — a 50° gap, by far the largest of any month. September is the most quiescent synoptic month of the year, which means local terrain effects dominate with minimal synoptic override. MDT snaps back to its NW signature while CXY drifts toward due-west.
When you filter observations to only hours with recorded precipitation, the wind signature flips completely. MDT's all-weather mean vector comes from 303° (NW). During precipitation hours, it comes from 76° (ENE) — a 227° reversal. CXY shifts similarly: from 281° (WNW) all-weather to 86° (E) during precip. Both stations converge on an east/ENE source during precipitation events, and the 18° gap between them nearly collapses to near-zero in spring and summer.
The gap between MDT and CXY collapses during precipitation: from 22° all-weather to just 10° during precip overall, and near-zero in spring and summer. This makes physical sense — precipitation in this region arrives predominantly on SE/E pre-frontal flow or in warm sectors, and that synoptic-scale forced advection overwhelms the local terrain channeling. Both stations see the same storm.
Central PA precipitation falls primarily in two synoptic setups. First, nor'easter and coastal low tracks that wrap easterly/ENE flow around the circulation — classic for heavy rain and snow events. Second, warm-sector convection where the low-level jet is from the SE/S, drawing Gulf moisture northward. In both cases the surface wind at both airports ends up from the east or ENE during the precipitation hours themselves. The NW flow that dominates the climatological record arrives after the storm passes — post-frontal and dry.
The winter divergence (MDT FROM 60° vs CXY FROM 82°, Δ=22°) hints that during winter precip events, CXY's river corridor funnels the easterly flow more tightly than MDT's open valley exposure — the orographic signature persists even during precipitation, just compressed.
| Season | MDT precip FROM | CXY precip FROM | Δ direction | MDT n | CXY n | Interpretation |
|---|---|---|---|---|---|---|
| All year | 76° ENE | 86° E | 10° | 79,529 | 82,781 | Strong convergence vs 22° all-weather gap |
| Spring | 82° E | 83° E | 1.6° | 24,162 | 25,223 | Stations nearly identical — terrain irrelevant |
| Summer | 129° SE | 128° SE | 0.6° | 13,858 | 15,494 | Perfect agreement — SE thunderstorm inflow |
| Fall | 52° NE | 76° ENE | 24° | 17,455 | 18,033 | More mixed precip types, orography re-emerges |
| Winter | 60° ENE | 82° E | 22° | 24,054 | 24,031 | CXY river corridor tightens E flow vs MDT |