Using wavelets to verify the scale structure of precipitation forecasts

Pub­lished in Adv. Stat. Clim. Mete­o­rol. Oceanogr., 6, 13–30, 2020:

Recent­ly devel­oped ver­i­fi­ca­tion tools based on local wavelet spec­tra can iso­late errors in the spa­tial struc­ture of quan­ti­ta­tive pre­cip­i­ta­tion fore­casts, there­by answer­ing the ques­tion of whether the pre­dict­ed rain­fall vari­abil­i­ty is dis­trib­uted cor­rect­ly across a range of spa­tial scales. This study applies the wavelet-based struc­ture scores to real numer­i­cal weath­er pre­dic­tions and radar-derived obser­va­tions for the first time. After tack­ling impor­tant prac­ti­cal con­cerns such as uncer­tain bound­ary con­di­tions and miss­ing data, the behav­iour of the scores under real­is­tic con­di­tions is test­ed in select­ed case stud­ies and analysed sys­tem­at­i­cal­ly across a large data set. Among the two test­ed wavelet scores, the approach based on the so-called map of cen­tral scales emerges as a par­tic­u­lar­ly con­ve­nient and use­ful tool: sum­ma­riz­ing the local spec­trum at each pix­el by its cen­tre of mass results in a com­pact and infor­ma­tive visu­al­iza­tion of the entire wavelet analy­sis. The his­togram of these scales leads to a struc­ture score which is straight­for­ward to inter­pret and insen­si­tive to free para­me­ters like wavelet choice and bound­ary con­di­tions. Its judge­ment is large­ly the same as that of the alter­na­tive approach (based on the spa­tial mean wavelet spec­trum) and broad­ly con­sis­tent with oth­er, estab­lished struc­tur­al scores.

Authors: Sebas­t­ian Buschow and Petra Friederichs

Read the full arti­cle here