A 3.5-Dimensional Variational Method for Doppler Radar Data Assimilation and Its Application to Phased-Array Radar Observations

Figure 1

Flowchart for the three steps of the method. Step 1 controls the quality of radial velocity observations 𝑣^o_r and produces radial velocity analyses 𝑣^a_r (on model grid) by minimizing 𝐽₁ in (6) at 𝑡₀ − 𝜏, 𝑡₀ and 𝑡₀ + 𝜏, respectively, for three consecutive radar volume scans. Step 2 produces the vector velocity increments 𝐯ⁱ by minimizing 𝐽₂ in (11) at 𝑡₀ − 𝜏/2 and 𝑡₀ + 𝜏/2, respectively. Step 3 produces the perturbation pressure increment 𝜋ⁱ by minimizing 𝐽_𝜋 in (16) first, and then produces the perturbation potential temperature increment 𝜃ⁱby minimizing 𝐽_𝜃 in (18) at 𝑡₀, and finally adjusts the water vapor mixing ratio 𝑞_v and the rain (or snow) mixing ratio 𝑞_r (or snow mixing ratio 𝑞_s) below (or above) the freezing level.