# Invert fluvial data set based on reference spectra catalogue The fluvial model inversion (FMI) routine uses a predefined look-up table with reference spectra to identify those spectra that fit the empirical data set best, and returns the corresponding target variables and fit errors. ```r fmi_inversion(reference, data, n_cores = 1) ``` ## Arguments - `reference`: `List` containing lists with precalculated model spectra. - `data`: `eseis` object or `numeric` matrix (spectra organised by columns), empiric spectra which are used to identify the best matching target parameters of the reference data set. - `n_cores`: `Numeric` value, number of CPU cores to use. Disabled by setting to 1. Default is 1. ## Returns `List` object containing the inversion results. ## Details Note that the frequencies of the empiric and modelled data sets must match. ## Examples ```r ## NOTE THAT THE EXAMPLE IS OF BAD QUALITY BECAUSE ONLY 10 REFERENCE ## PARAMETER SETS AND SPECTRA ARE CALCULATED, DUE TO COMPUATATION TIME ## CONSTRAINTS. SET THE VALUE TO 1000 FOR MORE MEANINGFUL RESULTS. ## create 100 example reference parameter sets ref_pars <- fmi_parameters(n = 10, h_w = c(0.02, 1.20), q_s = c(0.001, 8.000) / 2650, d_s = 0.01, s_s = 1.35, r_s = 2650, w_w = 6, a_w = 0.0075, f_min = 5, f_max = 80, r_0 = 6, f_0 = 1, q_0 = 10, v_0 = 350, p_0 = 0.55, e_0 = 0.09, n_0_a = 0.6, n_0_b = 0.8, res = 100) ## create corresponding reference spectra ref_spectra <- fmi_spectra(parameters = ref_pars) ## define water level and bedload flux time series h <- c(0.01, 1.00, 0.84, 0.60, 0.43, 0.32, 0.24, 0.18, 0.14, 0.11) q <- c(0.05, 5.00, 4.18, 3.01, 2.16, 1.58, 1.18, 0.89, 0.69, 0.54) / 2650 hq <- as.list(as.data.frame(rbind(h, q))) ## calculate synthetic spectrogram psd <- do.call(cbind, lapply(hq, function(hq) { psd_turbulence <- eseis::model_turbulence(h_w = hq[1], d_s = 0.01, s_s = 1.35, r_s = 2650, w_w = 6, a_w = 0.0075, f = c(10, 70), r_0 = 5.5, f_0 = 1, q_0 = 18, v_0 = 450, p_0 = 0.34, e_0 = 0.0, n_0 = c(0.5, 0.8), res = 100, eseis = FALSE)$power psd_bedload <- eseis::model_bedload(h_w = hq[1], q_s = hq[2], d_s = 0.01, s_s = 1.35, r_s = 2650, w_w = 6, a_w = 0.0075, f = c(10, 70), r_0 = 5.5, f_0 = 1, q_0 = 18, v_0 = 450, x_0 = 0.34, e_0 = 0.0, n_0 = 0.5, res = 100, eseis = FALSE)$power ## combine spectra psd_sum <- psd_turbulence + psd_bedload ## return output return(10 * log10(psd_sum)) })) graphics::image(t(psd)) ## invert empiric data set X <- fmi_inversion(reference = ref_spectra, data = psd) ## plot model results plot(X$parameters$q_s * 2650, type = "l") plot(X$parameters$h_w, type = "l") ``` ## Author(s) Michael Dietze

fmi_inversion function