Primjena tetrahoričkog i polihoričkog koeficijenta korelacijeu verifikaciji prognoza

The measure of association in 2 x 2 (K x K) contingency tables known as tetrachoric (polychoric) correlation coefficient is recalled. These measures rely on two assumptions: 1) there exist continuous latent variables underlying the contingency table and 2) joint distribution of corresponding standard normal deviates is bivariate normal. It is shown that, in practice, the tetrachoric (polychoric) correlation coefficient is an estimate of Pearson correlation coefficient between the latent variables. Consequently, these measures do not depend on bias nor on marginal frequencies of the table, which implies a natural and convenient partition of information (carried by the contingency table), between association, bias and probability of the event and subsequently enables the analysis of how other scores depend on bias and marginal frequencies. Results extended to K x K tables lead to eventual reduction in dimensionality from K2 to 2K. The theoretical findings are illustrated through analysis of real-life, 6 x 6 contingency tables on verification of quantitative precipitation forecasts.Tetrahorički (polihorički) koeficijent korelacije dobro je poznata mjera asocijacije u kontingencijskim tablicama veličine 2 x 2 (K x K). Ove mjere počivaju na dvjema pretpostavkama: 1) U pozadini kontingencijske tablice nalaze se neprekidne latentne varijable, te 2) zajednička funkcija distribucije pripadnih standardnih normalnih devijata je bivarijantna normalna razdioba. Pokazano je da tetrahorički, odnosno polihorički koeficijent korelacije predstavlja procjenu Pearsonovog koeficijenta korelacije izmedju latentnih varijabli. Posljedično, ove mjere ne ovise o pristranosti, kao ni o marginalnim čestinama, što rezultira rasčlambom informacije sadržane u kontingencijskoj tablici na tri dijela. Prvi se odnosi na povezanost, drugi na pristranost, a treći daje čestinu razmatrane pojave. Korištenjem dobivenog rastava analizirana je ovisnost drugih verifikacijskih mjera o pristranosti i o marginalnim čestinama. Rezultati su prirodno prošireni na tablice oblika K x K, pri čemu se dimenzija problema smanjuje s K2 na 2K. Teorija je primjenjena u analizi tablica veličine 6 x 6 koje opisuju kvantitativne prognoze oborine

The expectation of solution of random continuity equation with Gaussian velocity field

The continuity equation in d-dimensional space with random velocity field defined by means of a vector-valued Gaussian process is studied. The expectation of corresponding evolution family of operators is explicitly derived, generalizing in a sense the evolution family corresponding to the conventional diffusion equation

FIRST MEASUREMENTS OF BURA WIND AT SENJ WITH A THREE-AXIS ANEMOMETER

Measurements of the bora wind at Senj (east Adriatic) with a three-axis anemometer showed that at the periods smaller than 1 min turbulent eddies propagating downstream prevail, in accordance with conventional wisdom. At the periods of 5-10 min bora pulsations were observed, with rotary spectral analysis pointing to hithertho unsuspected dynamics of these pulsations

Ugniježđeno modeliranje istočno-jadranskih obalnih voda

The middle Adriatic coastal area was numerically modeled with a 1 km resolution in order to simulate temperature, salinity and currents. The model employed was a modification of the Princeton Ocean Model (POM), forced with surface momentum, heat and water fluxes and discharges from four rivers: Jadro, Žrnovnica, Cetina and Neretva. The coastal model was nested into the whole-Adriatic model having a 5 km resolution, using a simple off-line one-way nesting technique. Results of a three-year long experiment with perpetual atmospheric and river forcing were characterized by a strong annual signal, in reasonable agreement with temperature and salinity data taken at permanent oceanographic stations along the Split-Gargano transect. Current reversal obtained between the islands of Hvar and Vis in summer also agreed with previous measurements. The simulation also revealed the way Dalmatian islands – in particular Lastovo and Vis – influence the East Adriatic Current prevailing in winter, with wakes being formed behind the islands and jets among them. Comparison of an interannual simulation with corresponding measurements showed good agreement for temperature, whereas a discrepancy in salinity was related to the model being forced with climatological water fluxes. Experimental forecasts, produced over a six-month period, enabled some experience to be gained in operational oceanography, but also pointed to an additional problem – the model overmixing when the wind forcing is pronounced. Moreover, low spatial resolution of atmospheric forcing was suspected of reducing the quality of current forecasts for some wind directions.Obalno područje srednjeg Jadrana numerički je modelirano s rezolucijom od 1 km radi simuliranja temperature, saliniteta i struja. Upotrijebljeni model predstavljao je modifikaciju Princetonskog Oceanskog Modela (POM), kontroliranog površinskom izmjenom impulsa, topline i vlage te dotokom četiri rijeke: Jadra, Žrnovnice, Cetine i Neretve. Model obalnog područja povezan je s jadranskim modelom rezolucije 5 km, upotrebom jednostavnog načina gniježđenja. Rezultate trogodišnjeg eksperimenta izvedenog uz ponavljajuće atmosfersko i riječno djelovanje obilježio je jak godišnji signal, u prilično dobrom suglasju s temperaturnim i salinitetnim podacima prikupljenima na stalnim oceanografskim postajama uzduž profila Split-Gargano. Obrat struja dobiven u području između Hvara i Visa tijekom ljeta također je prethodno dokumentiran mjerenjima. Simulacija je uz to pokazala da dalmatinski otoci – napose Lastovo i Vis – utječu na istočno-jadransku struju zimi, dovodeći do pojave brazda iza otoka i mlazeva među njima. Usporedba rezultata simulacije višegodišnje promjenjivosti s odgovarajućim podacima ukazala je na dobro slaganje temperature, dok je relativno veliko odstupanje saliniteta bilo uzrokovano klimatološkim protocima vlage koji su nametnuti modelu. Eksperimen-talne prognoze, izdavane za razdoblje od šest mjeseci, omogućile su stjecanje iskustva u području operativne oceanografije, ali su upozorile i na jedan dodatni problem – pretjerano miješanje modelirano u situacijama u kojima je vjetar izražen. Osim toga, niska prostorna rezolucija upotrijebljenih atmosferskih polja po svoj je prilici nepovoljno utjecala na prognoze strujnog polja za neke smjerove vjetra

Desetodnevna varijabilnost ljetne cirkulacije u sjevernom Jadranu

Current, temperature and salinity data, collected during the ASCOP experiment that was carried out in the eastern part of the North Adriatic in summer 1989, have been analyzed together with related meteorological and hydrological data. After dividing the current series into three nearly equal subintervals, residual currents have been calculated for each of them. The major feature this exercise revealed was variability at a time scale of about ten days. A similar phenomenon has been observed by Italian researchers in the northeastern part of the Adriatic during several summers. It has been shown in the paper that the wind episodes registered during the experiment, although inducing remarkable changes in temperature and salinity records, did not directly generate the observed current variability. The changes in the Po River outflow have also been ruled out as the cause of the observed current reorientation. Temperature data collected in the area have pointed to stratification as the factor controlling the observed current variations. The stratification itself was influenced by buoyancy fluxes and wind forcing. However, further theoretical and empirical work is needed to establish conclusive evidence and elaborate dynamics of the observed phenomenon

Croatian high‑resolution monthly gridded dataset of homogenised surface air temperature

Homogenised climatological series and gridded data are the basis for climate monitoring and climate change detection. Considering this, monthly mean temperatures from 122 Croatian stations were homogenised, and high-resolution monthly gridded data were developed for the 1981–2018 period. Homogenisation needs to be performed on stations from the same climate region; therefore, hierarchical clustering is introduced to defne those climate regions in Croatia. The breaks of homogeneity were detected by the standard normal homogeneity test on 54 stations. Regression kriging was applied to produce monthly grids for each month in the analysed period. The quality of the interpolation assessed by leave-one-out cross-validation resulted in a root mean square error of 0.7 °C. The quality of spatial interpolation is supplemented with normalised error maps. The derived homogenised station data and monthly grids are necessary for national climate monitoring, the production of climate normals and the estimation of trends. After 1999, average annual anomalies from the 30-year climate standard normal 1981–2010 were positive and up to 1.4 °C warmer than the average and only occasionally negative. The measured amount, sign and signifcance of the trend were accurately captured on the trend maps calculated from the monthly maps. Signifcant strong warming was observed and mapped over the entire Croatian territory in April, June, July, August and November. It was stronger inland than on the coast. Annual trends were signifcant and ranged from 0.3 °C/decade to 0.7 °C/ decade. There was no observational evidence of enhanced elevation-dependent warming over elevations from 750 to 1594 m.Research of MPT was supported by employer, Croatian Meteorological and Hydrological Service, and by the project UKV − Carstic Coastal Water Management Endangered by Climate Changes (KK.05.1.1.02.0022). Open access funding is provided by Croatian Meteorological and Hydrological Service

Analiza zagrebačkih klimatoloških nizova pomoću empirijski određenih prirodnih sastavnih funkcija

The empirical mode decomposition method (EMD) (Huang, 1998) is applied to the series of annual and seasonal averages of temperature, cloudiness, air pressure and annual and seasonal sums of global radiation and precipitation, all observed in Zagreb-Gri~ in the period 1862–2002. The method itself decomposes the original series into so called intrincic mode functions (IMF), each being characterized by its own, intrinsic time scale. Sums of the low-frequency IMFs for the single element revealed present climatic fluctuations on the decade-to-century scale. It is confirmed that climatic fluctuations of every single element, particularly temperature and cloudiness, are the results of variations in the global atmospheric circulation above the whole Europe. Trend and long-term variations of Zagreb temperature fits to globally observed increase of temperature but also to variations of zonal circulation index. Exchange of Hadley’s zonal and Rossby’s wave regime of the general atmospheric circulation at the beginning of the 20th century is observed in the long-term variations of almost every element. Linear correlation coefficients between annual and seasonal long-term variations are calculated. It is shown that spring and winter variations mostly influenced annual fluctuations that is due to internal feed-back processes. Also, correlation coefficients for every pair of climatic element are calculated, enabling conclusions about interaction between elements on long-term scales.Metoda empirijskog rastavljanja (engl. empirical mode ecomposition) EMD, (Huang, 1998) primjenjena je na godišnje i sezonske nizove srednjaka temperature, tlaka, naoblake te godišnje i sezonske sume globalnog zračenja i količine oborine mjerene u Zagrebu-Grič, za razdoblje 1862–2002. Metoda rastavlja originalne nizove na tzv. prirodne sastavne funkcije, intrinsic mode functions (IMFs), od kojih je svaka karakterizirana svojstvenom vremenskom skalom. Međusobnom superpozicijom dugoperiodičnih prirodnih sastavnih funkcija pojedinog elementa uočena je prisutnost klimatskih fluktuacija. Potvrđeno je kako su klimatske fluktuacije svakog pojedinog elementa, posebno temperature i naoblake, rezultat varijacija opće cirkulacije atmosfere nad cijelom Europom. Trend i dugoperiodičke varijacije zagrebačke temperature dobro odgovaraju globalnom trendu općeg porasta temperature, ali i varijacijama zonalnog cirkulacionog indeksa. Pretpostavljena izmjena Hadleyevog zonalnog i Rossbyevog valnog režima opće cirkulacije atmosfere početkom 20. stoljeća očituje se u dugoperiodičkim varijacijama gotovo svih elemenata. Izračunati su koeficijenti linearne korelacije između godišnjih i sezonskih dugoperiodičnih varijacija te je pokazano kako se proljetne i zimske varijacije većine elemenata osjetno odražavaju na fluktuacije godišnjih srednjaka, što je u skladu s dominacijom internih procesa povratne sprege (engl. feed back). Također su izračunati koeficijenti korelacija između svaka dva klimatska elementa {to je omogućilo zaključke o interakcijama među elementima na dugoročnoj skali