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Polar Geophysical Institute has carried out monitoring of the surface gamma radiation background (GRB) arriving from the upper hemisphere at two stations (Apatity, Murmansk region, and Barentsburg, arch. Spitsbergen) since 2009. Two scintillation detectors on NaI(Tl) crystals are used. Their energy ranges are 20-400 keV and 0.2-5 MeV. In the first range there are output integral channels >20 keV and >100 keV. In the range of 0.2-5 MeV the differential energy spectrum is measured. The spectrum has a power form without any characteristic lines, which gives evidence that the radiation results from the interaction between secondary cosmic rays and the Earth’s atmosphere rather than from the radioactive elements decay. From the beginning of the measurements the increases of GRB associated with atmospheric precipitations were detected. The increase amplitude reaches 50% relative to the level measured before the precipitation. Further measurements and additional experiments have shown that these increases aren't connected with any radionuclides in precipitation or their emanation to the atmosphere during precipitation. The differential spectrum of the increase proper (the difference between spectra obtained during an increase (i.e. in precipitation) and during a clear weather before the increase) has an exponential form. The upper energy limit of the spectrum of increase is approximately at 2.5 MeV. We suggest a noncontradictory hypothesis to explain the effect of the GRB increase. It is based on the effect that the charged particles get additional energy in the electric fields of rain (not necessarily thunderstorm) clouds. Estimations have been made of the minimum electric field strength necessary to produce the increase observed. The values obtained do not exceed the electric field strength values directly measured in rain clouds.