Wind

Little Bat Instruments · revised 5 October 2026· draft

Abstract

Wind blowing over a rain gauge is pushed up and over its rim, and that updraft carries drops over the aperture that would otherwise have fallen in. Small drops go first, so light rain in a strong wind is undercaught worst. We model the airflow round the Midge with steady RANS CFD, fly raindrops through it size by size, and weight the result by how much water each size carries in real rain. At 2–8 m/s the bare Midge catches 96.2 %–98.8 % of light (1 mm/h) rain. A shield of eight leaves, 310 mm across, cuts what it misses at 5 m/s from 2.5 % to 0.9 %–1.7 %, as the wind meets a leaf or a gap: 1.3 % on average, 49 % of the bare gauge's loss won back.

Method

The method is the one the undercatch literature uses (Nešpor & Sevruk 1999; Colli et al. 2016), in three steps:

Airflow. Steady RANS (OpenFOAM simpleFoam, k-ω SST) round the gauge on its post, in a uniform wind, on a mesh of 1.07 million cells.
Drops. Raindrops flown through the time-averaged flow, size by size. For each size the catch efficiency (CE) is the number caught divided by the number still air would have delivered.
Rain. CE weighted by how much water each size carries in Marshall–Palmer rain at 1, 5, 20 mm/h.

The flow round the gauge

All three figures show the plane through the gauge's axis along the wind, with the wind blowing from the left. The gauge is drawn as the mesher saw it: the meshed surface cut by that plane. Hover (or tap) for the values at a point; the cross-hair follows in every figure.

Wind speed Loading…

Air speed and streamlines at 5 m/s. The air slows to almost nothing behind the gauge, and is pushed up and over the rim, speeding up above it (the far end of the key). Speed is in the plane; the cross-wind component changes it by under 1.5 % of the wind speed here.

Pressure coefficient, C_p = p / ½ρU². Red where the wind piles up against the gauge, blue where it is pulled away — over the rim and in the wake.

The updraft over the rim: what lifts drops clear of the aperture. Contours at 0.1, 0.2 and 0.3 of the wind speed. The strongest updraft over the aperture at 5 m/s is 0.77 of the wind speed.

caught blown clear carried in from outside the aperture

Raindrops of 0.35, 1 and 3 mm falling past the rim at 5 m/s, in time. Each size is released along the ten lines that, in still air, would land 0.2 aperture radii apart across the aperture, and along any line further out whose drops the wind carries in; each line releases a drop every 0.1 s. They are released where the pipeline releases its drops, 0.55 m above the rim or 0.6 m upwind of it, moving with the undisturbed wind. Filled drops are caught and fly on into the collector, stopping where they land: on its floor or — carried downwind by the eddy inside the bore — on its far wall, often just under the rim. Hollow ones are blown clear (their paths dashed). Ringed ones were aimed outside the aperture and are carried in. The updraft lifts drops aimed at the back of the aperture over it and carries in some aimed short of it, so the catchment slides upwind, and part of what is lost at the back is made up at the front — most of all for the small drops. The key counts both: drawn is every drop caught, wherever it was aimed, of the ten still air would deliver; plane measures the whole release line rather than counting lines; and aperture is the pipeline's, from its three-dimensional drop sheets (Table 2). Drops are flown in the plane through the axis by the site's own port of the pipeline's tracker, which agrees with it to within 2 mm on every drop tested.

How much rain it catches

Catch efficiency in Marshall–Palmer rain, by wind speed.

wind (m/s)	1 mm/h	5 mm/h	20 mm/h	max updraft / U
2	0.988	0.994	0.997	0.73
3.5	0.983	0.992	0.996	0.77
5	0.975	0.988	0.994	0.77
6.5	0.968	0.984	0.991	0.77
8	0.962	0.981	0.989	0.77

Catch efficiency by drop diameter. The smallest drops fall slowest and are carried off first.

drop (mm)	2 m/s	3.5 m/s	5 m/s	6.5 m/s	8 m/s
0.25	0.736	0.583	0.473	0.384	0.311
0.35	0.883	0.827	0.770	0.726	0.694
0.5	0.956	0.939	0.909	0.889	0.874
0.7	0.984	0.978	0.965	0.954	0.945
1	0.995	0.992	0.988	0.983	0.978
1.4	0.997	0.997	0.995	0.991	0.989
2	0.998	0.999	0.998	0.997	0.995
3	0.998	0.999	0.999	0.999	0.998
4	0.999	0.999	0.999	0.999	0.999
5.5	0.999	0.998	0.999	0.999	0.999

With a wind shield

The shield is eight leaves of 1.6 mm aluminium under a 3 mm ring round the tube, after the petals of a Tretyakov shield: each leaf climbs at 45° from the ring and bends flat for its outer 30 %, so its lip lies level with the rim. It is 310 mm across, 3.2 times the aperture (a Tretyakov is 6.6 times its own), and a quarter open: the gaps between the leaves take 25 % of the ring at every radius. In the mesh the sheet is 2.5 mm thick and its bends are sharp; the bolts are left out. The mesh has 1.45 million cells.

With eight leaves the catch depends on which way the wind blows. The pattern repeats every 45° and is mirror-symmetric, so a wind square onto a leaf and one square onto a gap, 22.5° round, are the two extremes, and the shield was run both ways at 2, 5, 8 m/s. Their mean is the estimate for a wind that may come from anywhere. In the figures below the three sit side by side, where the screen is wide enough: a leaf into the wind, a gap into it, and the two flows averaged node by node — where the leaf, there for half of it, is drawn faint.

Wind speed Loading…

A leaf into the wind

A gap into the wind

The mean of the two

Air speed and streamlines with the shield at 5 m/s: a leaf square to the wind, a gap, and the two flows averaged. The leaf turns the oncoming air up at its lip, well upwind of the aperture, and leaves a slow eddy over it. Through the gap the air reaches the tube and rises over the rim much as it does round the bare gauge (Figure 1), though the leaves either side of the plane still slow it.

A leaf into the wind

A gap into the wind

The mean of the two

Pressure coefficient with the shield at 5 m/s, as in Figure 2. With a leaf into the wind the air piles up against the leaf; through a gap, against the tube, and along the line of the leaves either side of the plane.

A leaf into the wind

A gap into the wind

The mean of the two

The updraft over the rim with the shield at 5 m/s, contours at 0.1, 0.2 and 0.3 of the wind speed. A leaf into the wind turns the air up at its lip, 155 mm upwind of the axis and clear of the aperture; through a gap it rises over the rim itself. The strongest updraft over the aperture is 0.41 of the wind speed with a leaf into the wind and 0.69 with a gap; bare, it is 0.77.

A leaf into the wind

A gap into the wind

The mean of the two

caught blown clear carried in from outside the aperture

Raindrops of 0.35, 1 and 3 mm falling past the shielded rim at 5 m/s, released and drawn as in Figure 4. The plane is one slice through the middle of the aperture, and with a shield it can catch more or less than the aperture as a whole: through a gap into a strong wind, much less. In the mean panel the drops fly through the averaged air, so its drawn and plane are the catch in that air; its aperture is the mean of the two runs' (Table 4).

Catch efficiency in Marshall–Palmer rain with the shield, and what it still misses as a share of what the bare gauge misses (1 / 5 / 20 mm/h).

wind (m/s)	gauge	1 mm/h	5 mm/h	20 mm/h	loss vs bare	max updraft / U
2	bare	0.988	0.994	0.997	1	0.73
	leaf into the wind	0.998	0.999	0.999	0.20 / 0.21 / 0.26	0.38
	gap into the wind	0.994	0.997	0.998	0.48 / 0.48 / 0.50	0.71
	mean of the two	0.996	0.998	0.999	0.34 / 0.34 / 0.38
5	bare	0.975	0.988	0.994	1	0.77
	leaf into the wind	0.991	0.996	0.998	0.35 / 0.38 / 0.39	0.41
	gap into the wind	0.983	0.992	0.995	0.68 / 0.71 / 0.75	0.69
	mean of the two	0.987	0.994	0.996	0.51 / 0.54 / 0.57
8	bare	0.962	0.981	0.989	1	0.77
	leaf into the wind	0.985	0.993	0.996	0.39 / 0.39 / 0.40	0.34
	gap into the wind	0.976	0.987	0.992	0.65 / 0.66 / 0.69	0.69
	mean of the two	0.980	0.990	0.994	0.52 / 0.52 / 0.54

Catch efficiency by drop diameter at 5 m/s, with and without the shield.

drop (mm)	bare	leaf into the wind	gap into the wind	mean of the two
0.25	0.473	0.798	0.593	0.695
0.35	0.770	0.926	0.864	0.895
0.5	0.909	0.972	0.946	0.959
0.7	0.965	0.988	0.977	0.982
1	0.988	0.994	0.990	0.992
1.4	0.995	0.999	0.996	0.997
2	0.998	0.998	0.998	0.998
3	0.999	1.001	0.999	1.000
4	0.999	1.000	0.999	1.000
5.5	0.999	0.999	0.999	0.999

At 5 m/s the bare Midge misses 2.5 % of light rain. With the shield it misses 0.9 % with a leaf into the wind and 1.7 % with a gap, 1.3 % on average: 0.35, 0.68 and 0.51 of the bare gauge's loss.

Not counted here is rain that lands on the shield and splashes or bounces into the aperture, the opposite of the wind's loss. A separate model of it on the same flow (OpenFOAM's splashBai wall model) puts it at the same order as the loss the shield removes, but its constants were fitted to fuel sprays on engine walls, not rain on aluminium. A side-by-side test in calm rain, where everything a shielded gauge reads over the bare one is splash-in, will settle it.

The bridged shield, in three dimensions

A gap into the wind is the leaves' weak orientation. Under the shield the wind piles up (C_p about +0.4 beneath the windward slot); over it the air is pulled away (about −0.5); and the slot between them vents the pocket as a narrow jet that rises up the slope at 1.2–1.3 times the wind speed and on into the windward rim. The fitted shield roofs each slot with a bridge: a third piece of sheet bolted on top of the two leaves' flat tips, so the lip runs unbroken round the shield, with a flap bent down at 25° over the slot to 78 mm in along it. The slot still vents, but under the flap rather than at the rim. At 5 m/s with a gap into the wind, the bridged shield misses 0.5 % of light rain, against 1.7 % without the bridges and 2.5 % bare.

Shade Show streamlines

75 mm below the aperture

Bare

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vertical air speed / wind speed (+ is up)

Bridged shield, a gap into the wind

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vertical air speed / wind speed (+ is up)

Bridged shield − bare

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change in vertical air speed / wind speed

Drag to turn the view; pinch, or scroll with ctrl (⌘) held, to zoom; right-drag or drag with two fingers to move it. Hover over the slice for the values there.

The air round the top of the gauge at 5 m/s, bare and with the bridged shield (a gap into the wind), in the box it was sampled in: 350 mm square, from 75 mm under the aperture to 45 mm over it. The arrow is the wind. It opens on the updraft 2.5 mm over the rim. Bare, the air rises over the windward rim at up to 0.8 of the wind speed and sinks over the back of the aperture. With the bridged shield the air over the windward rim sinks a little instead (−0.06 of the wind speed where it rose fastest bare), and the rising air is out at the shield's lip, 155 mm from the axis, at up to 0.7 of it: the third panel, the bridged shield's field less the bare gauge's node by node, shows both. The slice can shade the air speed instead, and lie level, along the wind or across it anywhere in the box; the gauge and shield are cut away on the near side of it, and their edges show faintly through it. The lines are streamlines of the averaged air from the same rake at the box's upwind face in both.

What is modelled, and what is not

Geometry: the outer tube with its 45° outside chamfer down to a knife edge at the bore; the well down to the debris mesh, treated as a floor; and the base, foot flanges, foot and the Ø100 mm round post. Fasteners are left out.
No ground: the gauge stands in open air. A gauge near the ground sits in a sheared, more turbulent wind; this setup measures what the gauge itself does to the flow.
Wind: uniform, along +x, 5 % turbulence intensity at the inlet. The bare gauge's answer depends on wind direction only through the foot's flanges, 240 mm below the rim; the shield's depends on it through its leaves, which is why it was run with a leaf and with a gap into the wind.
Steady RANS, averaged: the wake shed off the tube never settles, so the velocity is averaged over iterations 1200–2000. That gives the mean flow; turbulent gusts, which also scatter drops, are not modelled.
Drops: spheres whose drag is scaled to Gunn & Kinzer's measured terminal speeds; one-way coupled; released 0.55 m above the rim or 0.6 m upwind of it, where the air is within 0.5 % of the wind, moving with the wind; no splash-out or splash-in, no wetting loss.
Catch: a drop counts as caught if it comes down through the aperture plane inside the bore.

References

Colli, M., Lanza, L. G., Rasmussen, R. & Thériault, J. M. (2016). The collection efficiency of shielded and unshielded precipitation gauges. Part I: CFD airflow modeling. Journal of Hydrometeorology 17, 231–243.
Gunn, R. & Kinzer, G. D. (1949). The terminal velocity of fall for water droplets in stagnant air. Journal of Meteorology 6, 243–248.
Marshall, J. S. & Palmer, W. McK. (1948). The distribution of raindrops with size. Journal of Meteorology 5, 165–166.
Nešpor, V. & Sevruk, B. (1999). Estimation of wind-induced error of rainfall gauge measurements using a numerical simulation. Journal of Atmospheric and Oceanic Technology 16, 450–464.
Yang, D. et al. (1998). Accuracy of NWS 8″ standard nonrecording precipitation gauge: results and application of WMO intercomparison. Journal of Atmospheric and Oceanic Technology 15, 54–68.