Most large (over a kilometre in diameter) near-Earth asteroids are now known, but recognition that airbursts (or fireballs resulting from nuclear-weapon-sized detonations of meteoroids in the atmosphere) have the potential to do greater damage 1 than previously thought has shifted an increasing portion of the residual impact risk (the risk of impact from an unknown object) to smaller objects 2 . Above the threshold size of impactor at which the atmosphere absorbs sufficient energy to prevent a ground impact, most of the damage is thought to be caused by the airburst shock wave 3 , but owing to lack of observations this is uncertain 4,5 . Here we report an analysis of the damage from the airburst of an asteroid about 19 metres (17 to 20 metres) in diameter southeast of Chelyabinsk, Russia, on 15 February 2013, estimated to have an energy equivalent of approximately 500 (6100) kilotons of trinitrotoluene (TNT, where 1 kiloton of TNT 54.185310 12 joules). We show that a widely referenced technique 4-6 of estimating airburst damage does not reproduce the observations, and that the mathematical relations 7 based on the effects of nuclear weapons-almost always used with this technique-overestimate blast damage. This suggests that earlier damage estimates 5,6 near the threshold impactor size are too high. We performed a global survey of airbursts of a kiloton or more (including Chelyabinsk), and find that the number of impactors with diameters of tens of metres may be an order of magnitude higher than estimates based on other techniques 8,9 . This suggests a non-equilibrium (if the population were in a long-term collisional steady state the size-frequency distribution would either follow a single power law or there must be a size-dependent bias in other surveys) in the near-Earth asteroid population for objects 10 to 50 metres in diameter, and shifts more of the residual impact risk to these sizes. for the Chelyabinsk airburst, based on indirect illumination measured from video records. The brightness is an average derived from indirect scattered sky brightness from six videos proximal to the airburst, corrected for the sensor gamma setting, autogain, range and airmass extinction, following the procedure used for other airburst light curves generated from video 24,25 . The light curve has been normalized using the US government sensor data peak brightness value of 2.7 3 10 13 W sr 21, corresponding to an absolute astronomical magnitude of 228 in the silicon bandpass. The individual video light curves deviate by less than one magnitude between times 22 and 11.5 with larger deviations outside this interval. Time zero corresponds to 03:20:32.2 UTC on 15 February 2013. b, The energy deposition per unit height for the Chelyabinsk airburst, based on video data. The conversion to absolute energy deposition per unit path length assumes a blackbody emission of 6,000 K and bolometric efficiency of 17%, the same as the assumptions used to convert earlier US government sensor information to energy 26 . The heights are computed us...

The lightning flashes used in this work were mapped using data from the LO-FAR (LOw Frequency ARray) radio telescope. Due to its effective lightning protection system, LOFAR is able to continue to operate during thunderstorm activity[1]. The Dutch LOFAR stations consist of 38 (24 core + 14 remote) stations spread over 3200 km 2 in the northern Netherlands. The largest baseline between core stations is about 3 km, the largest baseline between remote stations is about 100 km. From each station we use 6 dual-polarized low band dipole antennas (LBA), sampled at 200 MHz, to observe the 30-80 MHz band. The raw time series data were saved to the transient buffer boards, which continuously buffer the last 5 s of data from a maximum of 48 dual-polarized antennas per station. The resulting relative timing accuracy is better than 1 ns. See [2] for more details on LOFAR. When a lightning flash occurs within the area enclosed by the Dutch LOFAR stations, as observed by www.lightningmaps.org, the transient buffer boards are stopped and the data is read to disk. The method we used to map each lightning flash has three major steps. In the first step we fitted plane-waves to the time of pulses received by individual LOFAR stations. Note that the LOFAR stations are less than 100 m in diameter and the lighting is many kilometers from the closest LOFAR station, so that a plane-wave approximation is very good for individual LOFAR stations. These plane-waves were used to identify non-functional antennas, and the intersection of their arrival directions gave a rough first estimate of the flash location, accurate to a few kilometers. Since each station has its own clock and cable delays, in the second step we found the clock offsets between the different LOFAR stations by simultaneously fitting the locations of multiple events and station clock offsets to the measured times of radio pulses, with a Levenberg-Marquardt minimizer. In order to achieve the highest precision, we chose to fit locations of 5 events that created pulses that were strong but not saturating, had a simple structure, and did not change shape significantly across different stations. After fitting, the root-mean-square difference between the modeled and measured arrival times of the radio pulses was around 1 ns. The resulting station clock offsets are consistent with LOFAR station clock calibrations, which are known

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