A weather radar system comprising: a transmitter configured to transmit a weather radar signal into a region of interest; a receiver configured to receive echoes scattered from the region of interest, and a computer system coupled at least with the receiver, wherein the computer system is configured to: calculate a plurality of attenuation pairs from the received echoes, wherein each attenuation pair comprises a cumulative attenuation and a differential attenuation from the received echoes; solve a cost function for each of the attenuation pairs, wherein the cost function returns a cost function value for each attenuation pair; and determine the attenuation pair associated with the minimum cost function value, characterised in that the cost function is a function of the differential propagation phase, the cumulative attenuation, and the differential attenuation, wherein the cost function comprises ∑ r = r 0 r m | φ dp r − φ dp r r | ⋅ ω, wherein ω = φ dp r Δ φ dp r 10 0.1 A h + A dp, φ dp represents the two-way differential propagation phase, φ dp r represents the reconstructed differential propagation phase, A h represents the two-way cumulative attenuation, and A dp represents the two-way differential attenuation. a transmitter configured to transmit a weather radar signal into a region of interest; a receiver configured to receive echoes scattered from the region of interest, and a computer system coupled at least with the receiver, wherein the computer system is configured to: calculate a plurality of attenuation pairs from the received echoes, wherein each attenuation pair comprises a cumulative attenuation and a differential attenuation from the received echoes; solve a cost function for each of the attenuation pairs, wherein the cost function returns a cost function value for each attenuation pair; and determine the attenuation pair associated with the minimum cost function value, characterised in that the cost function is a function of the differential propagation phase, the cumulative attenuation, and the differential attenuation, wherein the cost function comprises ∑ r = r 0 r m | φ dp r − φ dp r r | ⋅ ω, wherein ω = φ dp r Δ φ dp r 10 0.1 A h + A dp, φ dp represents the two-way differential propagation phase, φ dp r represents the reconstructed differential propagation phase, A h represents the two-way cumulative attenuation, and A dp represents the two-way differential attenuation. calculate a plurality of attenuation pairs from the received echoes, wherein each attenuation pair comprises a cumulative attenuation and a differential attenuation from the received echoes; solve a cost function for each of the attenuation pairs, wherein the cost function returns a cost function value for each attenuation pair; and determine the attenuation pair associated with the minimum cost function value, characterised in that the cost function is a function of the differential propagation phase, the cumulative attenuation, and the differential attenuation, wherein the cost function comprises ∑ r = r 0 r m | φ dp r − φ dp r r | ⋅ ω, wherein ω = φ dp r Δ φ dp r 10 0.1 A h + A dp, φ dp represents the two-way differential propagation phase, φ dp r represents the reconstructed differential propagation phase, A h represents the two-way cumulative attenuation, and A dp represents the two-way differential attenuation.