From an echo to millimetres per hour
A weather radar turns in circles, sending out short microwave pulses, and measures how much energy comes back from each point along the beam. That echo is the reflectivity, Z. Raindrops scatter in proportion to the sixth power of their diameter, so one 4 mm drop echoes as much as 4,096 drops of 1 mm. Z spans so many orders of magnitude that it is given in decibels: dBZ = 10 log₁₀ Z.
To get a rain rate R, assume a typical spread of drop sizes. The classic answer, from Marshall and Palmer in 1948, is Z = 200 R1.6: 20 dBZ is about 0.6 mm/h, 30 dBZ about 2.7 mm/h, 40 dBZ about 11 mm/h.
z = 10 ** (dbz / 10) # dBZ to Z (mm⁶/m³)
r_mp = (z / 200) ** (1 / 1.6) # Marshall–Palmer
plt.hist2d(dbz[wet], rate[wet], bins=(x_bins, r_bins), norm=LogNorm())
plt.plot(dbz_line, (10 ** (dbz_line / 10) / 200) ** (1 / 1.6))
The relation is a cloud, not a line. Drop sizes differ between drizzle, showers and melting snow, so at any reflectivity the rate can vary tenfold. Above 40 dBZ the measured rates stay far below the curve: hail and wet snowflakes echo strongly without being heavy rain, and rain products cap such echoes for that reason. A forecast scored on rain rates inherits all of this, which is one more reason to check it against rain gauges.
The beam rises with distance
The lowest beam of a radar points just above the horizon, typically half a degree up, and spreads to about one degree wide. The Earth curves away beneath it, while the air bends it slightly back down. The standard model treats this as a straight beam over an Earth of 4/3 its real radius.
def beam_height(r_km, elev_deg):
ke = 4 / 3 * 6371.0 # effective Earth radius
e = np.radians(elev_deg)
return np.sqrt(r_km**2 + ke**2 + 2 * r_km * ke * np.sin(e)) - ke
At 100 km the middle of the beam is already 1.5 km up, at 200 km more than 4 km. Winter drizzle and light rain from low clouds can fall entirely beneath it, so far from a radar light rain is missed or reported too weak. This is why networks place their radars close enough for their circles to overlap, and why rain is seen best where several radars look at it from near.
One European picture
Weather radars are run by national weather services, each network built for its own country. Most of them also share their images, and these are merged into composites for the whole continent: one picture of reflectivity, and one of rain rate, every 5 minutes. A Europe-wide nowcast starts from these composites. That is what makes one forecast for most of Europe possible, and also what sets its limits: a radar that does not send its images is a hole in the picture, even if it is working.
# share of the 5-minute composites each radar was part of
share = sorted((r["availability"] for r in radars.values()), reverse=True)
plt.bar(range(len(share)), share)
Most radars are there almost all the time. A long tail is not: radars are serviced, upgraded and replaced, sometimes for months, and some countries share only part of their network, or not all of the time. Where neighbouring radars overlap, a missing one is barely noticed; at the edge of a network it leaves a gap.
Where coverage is good, and where it is poor
- Good: flat or rolling country with dense, overlapping networks, where every place is within about 100 km of a radar. Much of western and central Europe is like this.
- Behind mountains, the beam is blocked. Alpine and Pyrenean valleys rely on radars placed to look into them, and rain on the far side of a ridge can be missed.
- Far out at sea and at the outer rim of the network, rain is only seen once it is close, and approaching rain appears late in the forecast.
- Where a country shares few of its radars, its territory is seen from neighbours far away, with the beam high and light rain missed.
- One feed: when the European composite stops, every forecast built only on it stops updating.
The coverage page shows Nimbo’s footprint on a map.
What radar cannot see well
- False echoes come from hills, wind farms, ships, birds and interference. They must be cleaned out before forecasting, or the nowcast moves rain that is not there.
- The bright band: where snow melts into rain, wet snowflakes echo like heavy rain, and a thin layer can look like a downpour.
- Snow reflects differently from rain, so amounts in winter and in the mountains are harder to get right.
- Heavy rain weakens the beam itself on its way through, so a storm behind another storm can look weaker than it is.
This is why a radar nowcast should also be checked against rain gauges on the ground (see how to measure a rain forecast).
Next: What is nowcasting?