Generation of analysis and consistent error fields using the Data Interpolating Variational Analysis (DIVA)

Abstract

The Data Interpolating Variational Analysis (Diva) is a method designed to interpolate irregularly-spaced, noisy data onto any desired location, in most cases on regular grids. It is the combination of a particular methodology, based on the minimisation of a cost function, and a numerically efficient method, based on a finite-element solver. The cost function penalises the misfit between the observations and the reconstructed field, as well as the regularity or smoothness of the field. The method bears similarities to the smoothing splines, where the second derivatives of the field are also penalised.The intrinsic advantages of the method are its natural way to take into account topographic and dynamic constraints (coasts, advection, . . . ) and its capacity to handle large data sets, frequently encountered in oceanography. The method provides gridded fields in two dimensions, usually in horizontal layers. Three-dimension fields are obtained by stacking horizontal layers.In the present work, we summarize the background of the method and describe the possible methods to compute the error field associated to the analysis. In particular, we present new developments leading to a more consistent error estimation, by determining numerically the real covariance function in Diva, which is never formulated explicitly, contrarily to Optimal Interpolation. The real covariance function is obtained by two concurrent executions of Diva, the first providing the covariance for the second. With this improvement, the error field is now perfectly consistent with the inherent background covariance in all cases.A two-dimension application using salinity measurements in the Mediterranean Sea is presented. Applied on these measurements, Optimal Interpolation and Diva provided very similar gridded fields (correlation: 98.6%, RMS of the difference: 0.02). The method using the real covariance produces an error field similar to the one of OI, except in the coastal areas.

Decline of the Black Sea oxygen inventory

“…The coefficients of Eq. (A1) can be determined from (1) the relative weights w i attributed to each observation d i , (2) the correlation length L and (3) the signalto-noise ratio λ (Troupin et al, 2012). The analyses presented in this study were achieved with equal weights w i = 1, L = 0.8…”

“…In short, the DIVA interpolation software (http://modb. oce.ulg.ac.be/mediawiki/index.php/DIVA; Troupin et al, 2012) computes a gridded climatology obtained by minimizing a cost function which penalizes gradients and misfits with observations. The DIVA detrending algorithm (Capet et al, 2014) computes trends for each year, i.e., the average difference between data pertaining to this year and the spatial analysis at these data locations.…”

“…The present study describes the application of the DIVA (Data-Interpolating Variational Analysis) detrending procedure (Troupin et al, 2012;Capet et al, 2014) to untangle the temporal and spatial variability of three indices related to the Black Sea oxygenation status: the depth and density level of oxygen penetration and the oxygen inventory. These values were diagnosed from a composite historical data set of oxygen vertical profiles.…”

Decorrelation scales for Arctic Ocean Hydrography. Part I: Amerasian Basin

“…Static interpolation approaches (e.g., optimal interpolation [Gandin, 1965;Reynolds and Smith, 1994], objective mapping [Wong et al, 2003;Böhme and Send, 2005;Böhme et al, 2008], and Data-Interpolating Variational Analysis [Troupin et al, 2010[Troupin et al, , 2012Korablev, 2014 in addition, exploit modeled physics and provide temporally and spatially varying 4-dimensional analysis fields. The former approaches need a scale representing the mean field, while the latter, in addition, needs spatial and temporal scales representing the anomaly field to fully exploit the information embedded in in-situ data.…”

Decorrelation scales for Arctic Ocean hydrography – Part I: Amerasian Basin

“…The present scale estimates pose a requirement from a basin-scale data assimilation on a sampling strategy. Static interpolation approaches (e.g., optimal interpolation (Gandin, 1965;Reynolds and Smith, 1994), objective mapping (Wong et al, 2003;Böhme and Send, 2005;Böhme et al, 2008), and data-interpolating variational analyses (Troupin et al, 2010(Troupin et al, , 2012Korablev, 2014) exploit statistical information of data to derive a mean analysis field. Data assimilation approaches, in addition, exploit modeled physics and provide temporally and spatially varying fourdimensional analysis fields.…”