Kalman filter and correction of the temperatures estimated by PRECIS model José Ruy Porto de Carvalho a, ⁎, Eduardo Delgado Assad a , Hilton Silveira Pinto b a Senior Researchers, Embrapa Informática Agropecuária, CP: 6041, CEP: 13083-886, Campinas, SP Brazil b CEPAGRI, Institute of Biology, Unicamp, SP Brazil article info abstract Article history: Received 7 April 2011 Received in revised form 8 July 2011 Accepted 11 July 2011 The purpose of this study is to evaluate the accuracy of the estimation the monthly mean temperature simulated by the PRECIS model—scenarios A2 and B2 of the IPCC—for Brazilian regions and to develop a Kalman filter to correct the systematic errors of the model for the months of January to June 2010. With a regionalized model, PRECIS aims to reproduce the main features of the climate in complex terrains. The temperature estimates for January to June 2010 are based on linear regression of PRECIS simulations in each pixel of the domain for two time periods, 1961–1990 and 2070–2100. These initial estimates are adapted to 1142 observing stations by a correction using the vertical temperature gradient of the Standard Atmosphere and the difference between model and real topography. The analysis was performed using monthly observed mean temperature data from meteorological stations, along with 1142 simulated data. The PRECIS model with systematic errors was ameliorated by the application of the filter resulting in an improved mean temperature prediction of 66% above the mean square error for the dry months and above 49% for the wet months, for both scenarios under study. At the half-way point, the improvement was 68% for the A2 scenario and 69% for scenario B2. © 2011 Elsevier B.V. All rights reserved. Keywords: State-space model Model systematic errors Climate prediction 1. Introduction Different statistical procedures are used in meteorology for adjusting the estimates of air temperature obtained by numeric forecasting models of climate. The linear regression methods were and are still widely used (Homleid, 2004; Glahn and Lowry, 1972). Regression techniques require a large set of data to efficiently compensate for systematic errors. The Kalman filter (Kalman, 1960; Kalman and Bucy, 1961) has the advantage of compensating systematic errors recursively in order to solve problems related to linear filtering of discrete data which does not require a data series. With the evolution of computing resources, the Kalman filter has become widely used to provide non-linear procedures (Chui and Chen, 2009) and allows its use with new tech- niques, such as generalized additive models (Wood, 2006; Vislocky and Fritch, 1995) or neural networks (Marzban, 2003). The theory of the Kalman filter provides equations to recursively modify the estimates of an unknown process, combining observations related to the process and knowl- edge about the temporal evolution (Homleid, 1995). This means that only the state estimated from the previous time step and the current measurement is needed to calculate the estimate for the current state. The past states can be esti- mated, as the state provided for the present and even future states. Given some initial values one can predict and adjust the model parameters by re-measurement, obtaining the estimated error on each update. These equations were initially developed in 1960 by Hungarian-American statistician RE Kalman in the context of the U.S. space program that would lead to the Apollo 11 moon mission in 1969. Its ability to incorporate the effects of errors and their computational structure gave the Kalman filter a wide field of application, especially with regard to trajectory analysis (Brown and Hwnag, 1997; Welch and Bishop, 2010; Faria and de Souza, 2010). Atmospheric Research 102 (2011) 218–226 ⁎ Corresponding author at: Embrapa Informática Agropecuária, CP: 6041, CEP: 13083-886, Campinas, SP Brazil. Tel.:+55 19 3211x5871; fax: +55 19 3211x5754. E-mail address: jruy@cnptia.embrapa.br (J.R. Porto de Carvalho). 0169-8095/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.atmosres.2011.07.007 Contents lists available at ScienceDirect Atmospheric Research journal homepage: www.elsevier.com/locate/atmos