We investigated features of corona point discharges when a grounded conductive rod is subject to a high background electric field. In the laboratory, high voltage is applied to an upper plate in a plane-to-point experiment, and the discharges are observed from a grounded rod using an ultraviolet camera and a photosensor. The current is measured using a shunt resistor, a current transformer, and a high impedance ammeter. We have found that corona current pulses have fast rise time (tens of nanoseconds) and slow decay (hundreds of nanoseconds). For the initial stage of the discharges, above a certain threshold, the frequency of pulses increases with the voltage applied. In the field, one current sensor coupled to a grounded rod, 1.5 m above a roof, was installed in a site located at an altitude of 2525 m above sea level. The same pulses observed in the laboratory are recorded during periods of electric field enhancement caused by the movement of charged clouds or lightning activity near the sensor. For that specific installation, the frequency of pulses is correlated with the ambient electric field measured 250 meters away. To the best knowledge of the authors, this is the first time in which such correlation is made for outdoor measurements, seeing that other works correlate the electric field with the average current flow. Pulses of positive corona were no longer observed when the electric field magnitude was lower than 1.8 kV/m and pulses of negative corona were more atypical and presented a higher threshold, of about 3.8 kV/m. This study is relevant for understanding the production of corona and space charges in high structures, such as wind turbine blades, towers, and buildings in general.