DIVA method

Barth A, Alvera-Azcárate A, Troupin C et al (2010) A web interface for griding arbitrarily distributed in situ data based on Data-Interpolating Variational Analysis (DIVA). Advances in Geosciences 28:29–37. https://doi.org/10.5194/adgeo-28-29-2010

Barth A, Beckers J-M, Troupin C et al (2014) Divand-1.0: N-dimensional variational data analysis for ocean observations. Geoscientific Model Development 7:225–241. https://doi.org/10.5194/gmd-7-225-2014

Beckers J-M, Barth A, Troupin C, Alvera-Azcárate A (2014) Some approximate and efficient methods to assess error fields in spatial gridding with DIVA (Data Interpolating Variational Analysis). Journal of Atmospheric and Oceanic Technology 31:515–530. https://doi.org/10.1175/JTECH-D-13-00130.1

Brankart J-M, Brasseur P (1998) The general circulation in the Mediterranean Sea: A climatological approach. Journal of Marine Systems 18:41–70. https://doi.org/10.1016/S0924-7963(98)00005-0

Brankart J-M, Brasseur. P (1996) Optimal analysis of in situ data in the Western Mediterranean using statistics and cross-validation. Journal of Atmospheric and Oceanic Technology 13:477–491. https://doi.org/10.1175/1520-0426(1996)013<0477:OAOISD>2.0.CO;2

Brasseur P (1994) Reconstruction de champs d’observations océanographiques par le Modèle Variationnel Inverse: Méthodologie et applications. PhD thesis, University of Liège

Brasseur P, Beckers J-M, Brankart J-M, Schoenauen R (1996) Seasonal temperature and salinity fields in the Mediterranean Sea: Climatological analyses of a historical data set. Deep-Sea Research I 43:159–192. https://doi.org/10.1016/0967-0637(96)00012-X

Brasseur P, Haus J (1991) Application of a 3-D variational inverse model to the analysis of ecohydrodynamic data in the Northern Bering and Southern Chukchi Seas. Journal of Marine Systems 1:383–401. https://doi.org/10.1016/0924-7963(91)90006-G

Brasseur PP (1991) A variational inverse method for the reconstruction of general circulation fields in the northern Bering Sea. Journal of Geophysical Research 96:4891–4907. https://doi.org/10.1029/90JC02387

Rixen M, Beckers J-M, Brankart J-M, Brasseur P (2000) A numerically efficient data analysis method with error map generation. Ocean Modelling 2:45–60. https://doi.org/10.1016/S1463-5003(00)00009-3

Optimal interpolation

Bretherton FP, Davis RE, Fandry C (1976) A technique for objective analysis and design of oceanographic instruments applied to MODE-73. Deep-Sea Research 23:559–582. https://doi.org/10.1016/0011-7471(76)90001-2

Cressman GP (1959) An operational objective analysis system. Monthly Weather Review 87:367–374. https://doi.org/10.1175/1520-0493(1959)087<0367:AOOAS>2.0.CO;2

Delhomme J (1978) Kriging in the hydrosciences. Advances in Water Resources 1:251–266. https://doi.org/10.1016/0309-1708(78)90039-8

Gandin LS (1965) Objective analysis of meteorological fields. Israel Program for Scientific Translations, Jerusalem

Gomis D, Ruiz S, Pedder M (2001) Diagnostic analysis of the 3D ageostrophic circulation from a multivariate spatial interpolation of CTD and ADCP data. Deep-Sea Research 48:269–295. https://doi.org/10.1016/S0967-0637(00)00060-1

Hartman L, Hössjer O (2008) Fast kriging of large data sets with Gaussian Markov random fields. Computational Statistics & Data Analysis 52:2331–2349. https://doi.org/10.1016/j.csda.2007.09.018

Kaplan A, Kushnir Y, Cane MA (2000) Reduced space optimal interpolation of historical marine sea level pressure: 1854-1992*. Journal of Climate 13:2987–3002. https://doi.org/10.1175/1520-0442(2000)013<2987:RSOIOH>2.0.CO;2

Krige DG (1951) A statistical approach to some basic mine valuation problems on the Witwatersrand. Journal of the Southern African Institute of Mining and Metallurgy 52:119–139

McIntosh PC (1990) Oceanographic data interpolation: Objective analysis and splines. Journal of Geophysical Research 95:13529–13541

Ooyama KV (1987) Scale-controlled objective analysis. Monthly Weather Review 115:2479–2506. https://doi.org/10.1175/1520-0493(1987)115<2479:SCOA>2.0.CO;2

Shen S, Smith T, Ropelewski C, Livezey R (1998) An optimal regional averaging method with error estimates and a test using tropical pacific SST data. Journal of Climate 11:2340–2350. https://doi.org/10.1175/1520-0442(1998)011<2340:AORAMW>2.0.CO;2

Zhang H, Wang Y (2010) Kriging and cross-validation for massive spatial data. Environmetrics 21:290–304. https://doi.org/10.1002/env.1023

Spline interpolation

Craven P, Wahba G (1978) Smoothing noisy data with spline functions. Numerische Mathematik 31:377–403. https://doi.org/10.1007/BF01404567

Franke R (1985) Thin plate splines with tension. Computer Aided Geometric Design 2:87–95. https://doi.org/10.1016/0167-8396(85)90011-1

Schweikert DG (1966) An interpolation curve using a spline in tension. Journal of Mathematics and Physics 45:312–317

Wahba G (1975) Smoothing noisy data with spline functions. Numerische Mathematik 24:383–393

Wahba G, Wendelberger J (1980) Some new mathematical methods for variational objective analysis using splines and cross validation. Monthly Weather Review 108:1122–1143

Climatologies and applications

Bhaskar TVSU, Jayaram C, Rao EPR (2012) Comparison between Argo-derived sea surface temperature and microwave sea surface temperature in tropical Indian Ocean. Remote Sensing Letters 4:141–150. https://doi.org/10.1080/2150704X.2012.711955

Capet A, Troupin C, Carstensen J et al (2014) Untangling spatial and temporal trends in the variability of the Black Sea Cold Intermediate Layer and mixed Layer Depth using the DIVA detrending procedure. od 64:315–324. https://doi.org/10.1007/s10236-013-0683-4

Denis-Karafistan A, Martin J-M, Minas H et al (1998) Space and seasonal distributions of nitrates in the mediterranean sea derived from a variational inverse model. dsr1 45:387–408. https://doi.org/10.1016/S0967-0637(97)00089-7

Karafistan A, Martin J-M, Rixen M, Beckers J-M (2002) Space and time distributions of phosphates in the Mediterranean Sea. dsr1 49:67–82. https://doi.org/10.1016/S0967-0637(01)00042-5

Rixen M, Beckers J-M, Allen J (2001) Diagnosis of vertical velocities with the QG Omega equation: A relocation method to obtain pseudo-synoptic data sets. dsr1 48:1347–1373. https://doi.org/10.1016/S0967-0637(00)00085-6

Rixen M, Beckers J-M, Levitus S et al (2005a) The Western Mediterranean Deep Water: A proxy for global climate change. grl 32:L12608. https://doi.org/10.1029/2005GL022702

Rixen M, Beckers J-M, Maillard C, MEDAR Group (2005b) A hydrographic and bio-chemical climatology of the Mediterranean and the Black Sea: a technical note on the use of coastal data. Bollettino di Geofisica Teorica e Applicata 46:319–327

Teague WJ, Carron MJ, Hogan PJ (1990) A comparison between the Generalized Digital Environmental Model and Levitus climatologies. jgr 95:7167–7183. https://doi.org/:10.1029/JC095iC05p07167

The MEDAR group (2005) A Mediterranean and Black Sea oceanographic database and network. Bollettino di Geofisica Teorica ed Applicata 46:329–343

Troupin C, Machín F, Ouberdous M et al (2010) High-resolution climatology of the north-east atlantic using data-interpolating variational analysis (diva). jgr 115:C08005. https://doi.org/10.1029/2009JC005512

Tyberghein L, Verbruggen H, Klaas P et al (2012) ORACLE: A global environmental dataset for marine species distribution modeling. Global Ecology and Biogeography 21:272–281. https://doi.org/10.1111/j.1466-8238.2011.00656.x

Yari S, Kovac̆ević V, Cardin V et al (2012) Direct estimate of water, heat, and salt transport through the Strait of Otranto. jgr 117:C09009. https://doi.org/10.1029/2012JC007936

Others

Chilès J-P, Delfiner P (1999) Geostatistics: Modeling spatial uncertainty, 1st edn. Wiley-Interscience

Girard D (1989) A fast Monte-Carlo cross-validation procedure for large least squares problems with noisy data. Numerische Mathematik 56:1–23. https://doi.org/10.1007/BF01395775

Matheron G (1963) Principles of geostatistics. J Chem Metall and Min Soc South Africa 52:119–139

Steele M, Morley R, Ermold W (2001) PHC: A global ocean hydrography with a high-quality Arctic Ocean. Journal of Climate 14:2079–2087. https://doi.org/10.1175/1520-0442(2001)014<2079:PAGOHW>2.0.CO;2

Storch H von, Zwiers F (1999) Statistical analysis in climate research. Cambridge University Press, Cambridge

Tandeo P, Ailliot P, Autret E (2011) Linear Gaussian state-space model with irregular sampling: Application to sea surface temperature. Stochastic Environmental Research and Risk Assessment 25:793–804. https://doi.org/10.1007/s00477-010-0442-8

Troupin C, Sirjacobs D, Rixen M et al (2012) Generation of analysis and consistent error fields using the Data Interpolating Variational Analysis (Diva). Ocean Modelling 52-53:90–101. https://doi.org/10.1016/j.ocemod.2012.05.002