2. Indian Institute of Tropical Meteorology (IITM), MoES Suryachandra A. Rao (Some Slides are taken from Web) Numerical Atmosphere, Ocean and Coupled Modelling SASCOF Training Workshop on Seasonal Forecasting (14-21 April 2014)

3. Outline of the Presentation  Dynamical Prediction  Atmospheric General Circulation Model (Tier-Two approach)  Coupled Ocean-Atmosphere General Circulation model (Tier-one approach)  Ocean Models

6. Dynamical Predictions (Tier-2 or Tier-1?)  Tier-Two Models: Atmospheric General Circulation Models  Integration with prescribed SST boundary conditions  Atmospheric Initial Conditions  Tier-One Models: Coupled Ocean-Land- Atmosphere Models

7. Why Modelling?  To ESTIMATE the state of the system:  ANALYSES=OBSERVATIONS+MODEL  To FORECAST the future state  To SUMMARISE our understanding  (MODEL=THEORY/MAP OF REALITY)

8. Model Definition  A model is only a representation of reality (e.g. a street plan of reality)  Good modellers know the strong AND weak points of their models Some quotations:  All models are wrong, but some are useful - George Box  The purpose of models is not to fit the data but to sharpen the questions - Samuel Karlin  A theory has only the alternative of being right or wrong. A model has a third possibility, it may be right, but irrelevant. - Manfred Eigen

9. Modelling Process

10. Modelling Driving Factors

11. Brief History of Modelling

14. Electronic Numerical Integrator and Computer

15. MoES AADITYA (790 TF)

16. Dynamical Equations

17. Basic equations

18. Basic Equation Set Horizontal Momentum Equations φ = latitude, a = radius of the Earth, Ω = rotational frequency of Earth, F = friction advection terms curvature terms friction Coriolis termspres. grad. time derivs.

19. Basic Equation Set Vertical Momentum Equation φ = latitude, a = radius of the Earth, Ω = rotational frequency of Earth, F = friction advection terms curvature term friction Coriolis termpres. grad. time deriv. gravity

20. Basic Equation Set Thermodynamic Equation γ = lapse rate of temperature, γ d = dry adiabatic lapse rate, Q = diabatic heating rate advection terms dry adiabatic term diabatic heating time deriv. or, alternately…

21. Basic Equation Set Continuity Equations (i.e., mass – top – and water vapor – bottom – are neither created nor destroyed) q v = water vapor mixing ratio, Q v = source/sink of qv due to phase changes advection termstime derivs. divergence term

22. Basic Equation Set Ideal Gas Law

23. If you can solve the set of equations (often referred to as the primitive equations) given in the past few slides, you can do NWP! …but… …how do we actually solve these equations???

24. What Do We Need? How do we represent these equations on a map? How do we integrate them in time? How do we integrate them in space? How do we handle resolvable versus unresolvable processes? How do we handle diabatic processes? How do we handle friction? How do we handle microphysical phase changes (water vapor as well as other species – cloud, ice, graupel, rain, etc.)? How do we obtain our initial atmospheric state? …all among many relevant questions we will address!

25. Another scary thought: Nearly everything we describe from here on out involves some sort of approximation. This is true for the equations themselves, the methods used to solve them, the initial and boundary data used to drive the model, and so on.

26. Prognostic vs. Diagnostic Prognostic: any equation with a time-derivative is a prognostic equation; it can be integrated in time to produce a prediction Diagnostic: any equation without a time-derivative is a diagnostic equation; it can only be used to diagnose what is happening at a given time

27. This equation is solved for a three- dimensional “matrix” of points (or a grid) that covers the atmosphere from the surface to some level near the top of the atmosphere. Here is a 2-dimensional slice through the grid……..

28. Ground ……………………………………………… ……………………………………………… ……………………………………………… ……………………………………………… ……………………………………………… ……………………………………………… 100 millibars Grid points Computational levels East-West Distance  Altitude 

29. Horizontal grid structures MM5 and othersWRF and others From Randall (1994)

30. HexagonalTriangular From ccrma.standford.edu/~bilbao

31. Unstructured: Omega Model From Boybeyi et al. (2001)

32. Domains Shape From Rife et al. (2004) From mitgcm.org (2006) Spherical Nested grids

33. Finite Difference methods Stability, Accuracy and Convergence

34. Real World Problem

35. What should be parameterized ?  Radiation transfer.  Surface processes.  Vertical turbulent processes.  Clouds and large-scale condensation.  Cumulus convection.  Gravity wave drag. 16 major physical processes in climate system. (from http://www.meted.ucar.edu/nwp/pcu1/ic4/frameset.htm) Model Physics include:

36. How do we do parameterization in numerical models?  Ignore some processes (in simple models).  Simplifications of complex processes based on some assumptions.  Statistical/empirical relationships and approximations based on observations.  Nested models and super- parameterization: Embed a cloud model as a parameterization into climate models.

37. Cumulus convective Parameterization schemes  Manabe moist convective adjustment scheme.  Arakawa – Schubert scheme.  Betts – Miller scheme.  Kuo scheme. Early stage of cumulus development. Mature stage of cumulus development. This storm has reached an upper-level inversion, forming an anvil-shape to the cloud.

38. Probabilistic-Ensemble NWP ● There are several ways to produce probabilistic information but the most viable and popular is ensemble prediction. ● Instead of running one forecast, run a collection (ensemble) of forecasts, each starting from a different initial state or with different physics. ● The variations in the resulting forecasts can be used to estimate the uncertainty of the prediction. ● The ensemble mean is on average more skillful than any individual member.

39. e a u c j t g n M T T Analysis Region 48h forecast Region 12h forecast 36h forecast 24h forecast

40. Useful References: Ocean modeling Haidvogel and Beckmann, Numerical Ocean Circulation Modeling, Imperial College Press, 1999. Kantha and Clayson, Numerical Models of Oceans and Oceanic Processes, Academec Press, 2000. Griffies, Fundamentals of ocean climate models, Princeton Univ. Press, 2004.Forecasting and data assimilation: Mooers (Ed.), Coastal Ocean Prediction, Coastal & Estuarine Studies Ser., 56, AGU Publ., 1999. Pinardi and Woods (Eds.), Ocean Forecasting: Conceptual Basis and Applications, Springer, 2002. Fu and Cazenave (Eds.), Satellite Altimetry and Earth Sciences, International Geophys. Ser., 69, Academic Press, 2001. (chapter 5 on data assimilation)

42. History of Ocean Modelling Note that advances in ocean prediction systems is decades behind atmospheric weather forecasting: Numerical weather forecasting started in the 1950s (Charney, von Neumann and others) Ocean forecasting only in the 1980s-1990s! Why? -public demand? -oceanic scales -data availability -data assimilation methodologies -insufficient computational capabilities

43. Why to do Ocean Modelling? The ocean is a geophysical fluid The goal of ocean modeling is to reproduce numerically the dynamics of the ocean Dynamics of the ocean include: mean and time varying circulation, waves, turbulence, instabilities, convection, mixing, jets, etc. Cannot do ocean modeling without understanding geophysical fluid dynamics and numerical methods!

44. what scales of motion do we want to model? –large-scale when considering the large-scale –stratification –rotation

45. Scales of Motion

48. Importance of Rotation

49. Importance of Stratification

54. Various Steps Involved in Ocean Modelling

55. Ocean Model Types

56. Vertical coordinates

57. Idealized Representation of Model Vertical Coordinates

59. INGV - Istituto Nazionale di Geofisica e Vulcanologia - Italy Sea Ice Oceans The Climate System Biosphere Soil Moisture Run-off Atmosphere Precipitation Evaporation

60. INGV - Istituto Nazionale di Geofisica e Vulcanologia - Italy Coupled Phenomena Teleconnections The interactions between atmosphere and oceans in the tropics dominate the variability at interannual scales. The Sea Surface Temperature affects the atmosphere generating giant patterns that extend over the planet Thermohaline Circulation The deep oceanic circulations is driven by fluxes of heat and fresh water that change temperature and salinity of the water. Dense water (cold and saline) sink deep down creating a worldwide circulation as light water (fresh and warm) upwells through the world ocean, affecting the global sea surface temperatures, which in turn change the dominant mode of climate variability through the teleconnections. Why is there a need for considering coupled models ? There are at least two major reasons why it is clear that realistic description of climate cannot be done without considering the atmosphere and ocean at the same time

61. INGV - Istituto Nazionale di Geofisica e Vulcanologia - Italy SST The interactions between atmosphere and oceans in the tropics dominate the variability at interannual scales. The main player is the variability in the equatorial Pacific. Wavetrains of anomaly stem from the region into the mid-latitudes, as the Pacific North American Pattern (PNA). The tropics are connected through the Pacific SST influence on the Indian Ocean SST and the monsoon, Sahel and Nordeste precipitation. It has been proposed that in certain years the circle is closed and and a full chain of teleconnections goes all around the tropics. Also shown is the North Atlantic Oscillation a major mode of variability in the Euro_atlantic sector whose coupled nature is still under investigation. PNA NAO North Atlantic Oscillation Sahel Nordeste Monsoon SST Teleconnections PNA

62. INGV - Istituto Nazionale di Geofisica e Vulcanologia - Italy The interactions between atmosphere and ocean in the high latitudes drive the long term circulation of the deep ocean. Cold, dense water sinks int he north Atlantic and in the Antarctica and fills the ocean basins before reemerging as warm surface waters. Thermohaline Circulation Based on a CLIVAR transparency Model studies have shown that other circulation are possible with sinking taking place in the North Pacific as well. We do not know if this possibility has ever been realized during the history of the planet.

63. INGV - Istituto Nazionale di Geofisica e Vulcanologia - Italy Numerical Models The only hope we have to be able to understand and possibly predict some of these changes is to use numerical models to investigate the dynamics of atmosphere-ocean dynamics. Atmospheric and ocean numerical models can be put together (coupled) and numerically integrated for hundreds or thousands of years, depending on the realism of the models involved

64. INGV - Istituto Nazionale di Geofisica e Vulcanologia - Italy Oceans -- Soil -- Cyosphere -- Biosphere COOLING HEATING Laten Heat Wind Stress RAIN EVAPORATION Sensible Heat REFLECTION EMISSION ABSORPTION TRASPORTO PRESSIONE Radiation Temperature Water Vapor TRANSPORT Solar Radiation Earth Radiation Wind

65. INGV - Istituto Nazionale di Geofisica e Vulcanologia - Italy Atmosphere Laten Heat Flux Wind Stress RAIN EVAPORATION Sensible Heat TemperatureCurrents TRANSPORT Solar Radiation Salinity TRANSPORT Atmospheric radiation Density

66. INGV - Istituto Nazionale di Geofisica e Vulcanologia - Italy Discretization Methods The atmosphere and the ocean are divided in computational cells: (Temperature, Wind, Rain, Sea Ice, SST, Salinity, … ) both horizontally and vertically. Dimension of the cell (resolution) 200-300 km The dimensions of the cell are usually not the same in the atmosphere and ocean component because of the different dynamics.

67. INGV - Istituto Nazionale di Geofisica e Vulcanologia - Italy Oceans -- Sea Ice Atmosphere Wind StressPrecipitation Solar Radiation Atmospheric Radiation Air Temperature Sea Surface Temperature Sensible Heat FluxLatent Heat Flux Wind StressFresh Water Flux Surface Temperature COUPLER: (1) Interpolate from the atmospheric grid to the ocean grid and viceversa. (2) Compute fluxes

68. Very Large Compiuters are needed Project of the Earth Simulator Computer (Japan) : objective, a global coupled model with 5km resolution

69. INGV - Istituto Nazionale di Geofisica e Vulcanologia - Italy The main problem is how to synchronize the time evolution of the atmosphere with the evolution of the ocean. The most natural choice is to have a complete synchronization (synchronous coupling): This choice would require to have similar time steps for both models, for instance 30min for the atmospheric model and 2 hours for the ocean model. Computationally very expensive Atmosphere Ocean Coupling tt tt tt tt tt tt tt tt

70. INGV - Istituto Nazionale di Geofisica e Vulcanologia - Italy Another possibility is to exploit the different time scales using the fact that the ocean changes much more slowly than the atmosphere (asynchronous coupling): Atmosphere Ocean Coupling tt Integrate for a very long time This choice save computational time at the expense of accuracy, but for very long simulations (thousands of years) may be the only choice. Coupling tt Integrate for a very long time

71. INGV - Istituto Nazionale di Geofisica e Vulcanologia - Italy Coupling Start of integration Coupling Integrate the coupled model for a period, e.g. two years, but impose observed surface temperature and salinity Start of integration Coupling Spin-up the ocean with observed atmospheric forcing Robust Diagnostic Spin-up But sometimes the models are simply started from climatological conditions or, in the case of climate change experiments, the procedure may become much more sophisticated to account for effects from soil and ice.

72. INGV - Istituto Nazionale di Geofisica e Vulcanologia - Italy Balancing the simulations Coupled model are much more sensitive than either ocean or atmosphere model alone. There no constraints imposed, as the SST for the atmospheric simulations or the surface winds for the ocean, that can help in guiding the model toward a realistic climate state. The only forcing is given by the external solar radiation and the model must be capable of realizing its own balanced climate state. The model drift from the initial condition as it slowly reaches for its own equilibrium, if the model is realistic the final equilibrium will be very similar to the what we think is the present Earth climate, if the initial condition is well balanced the drift will be small and smooth. 0100200 Years of Simulations

73. INGV - Istituto Nazionale di Geofisica e Vulcanologia - Italy What coupled models can do The first coupled models had large drifts to an unrealistic climate state. It was then proposed to include a correction to partially correct for the poor fluxes that were exchanged between the models. This correction, known as “flux-adjustment” allowed early experiments, but is becoming less necessary in modern models. The following slides will show some of the results from an integration of a coupled model, developed at our institution in collaboration with LODYC in Paris, within the context of a project sponsored by the European Union, SINTEX. The results are however pretty typical of the behaviour of coupled models.

74. INGV - Istituto Nazionale di Geofisica e Vulcanologia - Italy The SINTEX coupled model Atmosphere ECHAM-4 Coupler OASIS Ocean OPA ECHAM-4: Max-Planxk -Institute, Hamburg Roeckner et al., 1996) Global Spectral T30 (3.75 x 3.75 deg) 19 Vertical levels OPA 8.1: LODYC, Paris, Madec et al., 1998) Global 2 deg longitude 0.5 - 2 deg latitude 31 Vertical Levels Climatological Sea Ice Coupling every 3 Hours No Flux Adjustment

75. INGV - Istituto Nazionale di Geofisica e Vulcanologia - Italy Precipitation Coupled models can reproduce precipitation pretty well on a global scale, including the tropical ITCZ and monsoon circulation, but the pattern follow too much the seasonal oscillation of the sun The rain is too much concentrated in the summer hemisphere and the South Pacific Convergence Zone does not have the right shape

76. INGV - Istituto Nazionale di Geofisica e Vulcanologia - Italy Sea Surface Temperature Marine Temperature in the model are too narrowly confined to the equator, the observations are wider Observations Model Coupled models can reproduce the over-all pattern, but they tend to be warmer than observations in the eastern oceans and colder in the western portions of the oceans

77. INGV - Istituto Nazionale di Geofisica e Vulcanologia - Italy Southern Oscillation Coupled models can reproduce the strong coupling between Sea Level Pressure and Sea Surface Temperature as it is shown in this 200 years time series of the Southern Oscillation Index (SOI) and of the SST in the NINO3 area from a simulation. The anticorrelation is pretty clear and the model display a realistic interannual variability

78. INGV - Istituto Nazionale di Geofisica e Vulcanologia - Italy Teleconnections Correlations between the Sea Level Pressure in Darwin and global SLP in the coupled model. The correlations are very realistic Correlations between the Sea Level Pressure in Darwin and global SST in the coupled model. Also in this case the basic teleconnections are there, but the quality is barely satisfactory. Correlations between the Sea Level Pressure in Darwin and global SST in the coupled model. Also in this case the basic teleconnections are there, but the quality is barely satisfactory.

79. INGV - Istituto Nazionale di Geofisica e Vulcanologia - Italy Correlations between the Sea Surface Temperature in the equatorial Pacific (NINO3) and global SST. Results from observations and two 200 years simulations of coupled model are shown, at lower resolution and at a higher resolution. The models reproduce global patterns, but the propagation of the teleconnections into the midlatitude is still poorly represented. Teleconnections Observations Low Resolution High Resolution

80. INGV - Istituto Nazionale di Geofisica e Vulcanologia - Italy Empirical Orthogonal Patterns from coupled models, atmospheric- only models and observations. It is here shown the first EOF for Winter (JFM) Z500. The models, especially the high resolution coupled model, shows a good resemblance with observations, indicating that the modes of variability of the model are close to the real one. Variability (I) Coupled Model High Resolution Coupled Model Low Resolution Observations Atmospheric Model Low Resolution

81. INGV - Istituto Nazionale di Geofisica e Vulcanologia - Italy Empirical Orthogonal Patterns from coupled models, atmospheric- only models and observations. It is here shown the second EOF for Winter (JFM) Z500. This is interesting to show that aldo the higher order modes are captured and that the partition of variance between the modes is also realistic. Variability (II) Coupled Model High Resolution Coupled Model Low Resolution Observations Atmospheric Model Low Resolution

82. 81 Climate modeling 2. The Simplest Climate Model: 0-dimensional energy balance model

83. 82 Climate modeling 1) How much energy is reaching the top of the atmosphere from the sun? The solar flux received at the top of the atmosphere from the sun depends on the distance of the Earth from the sun. The average value of this flux is called the solar constant, S 0, and has a value of 1367 Wm -2. Note that this value varies as the orbit of the Earth around the sun is not a perfect circle. S0S0 1367 Wm -2 Energy Absorbed by the Atmosphere (1)

84. 83 Climate modeling 2) How much energy is directly reflected back to space? Some of the solar flux arriving on Earth is directly reflected back to outer space by clouds and the Earth surface. Clouds have a very high albedo * (up to 0.8). Taking all reflectors (clouds, ground, sea) together, the Earth has an albedo of approximately 0.3. Hence only 70 % of the solar flux arriving on earth is available to the system. S0S0 A E *S 0 Energy Absorbed by the Atmosphere (2) Albedo comes from a Latin word for “whiteness”

85. 84 Climate modeling The flux we used so far describes the energy per unit area, hence we now know how much energy per square meter is available to the Earth from solar radiation. To calculate the total energy absorbed we need to multiply the flux with the area that intercepts that radiation. As we can see, that area (the shadow area) is a disk with the radius of the Earth: Energy Absorbed by the Atmosphere (3) 3) What is the total energy absorbed by the Earth?

86. 85 Climate modeling Energy Absorbed by the Atmosphere (4) Total energy absorbed Solar flux at TOA Reflected flux Area of a disk with radius of the earth or after some minor rearrangement :

87. 86 Climate modeling For a good estimate of this number, we can assume that the Earth is a blackbody. By making that assumption we can now use the Stefan- Boltzmann law to calculate the flux of longwave (infrared) radiation as: Energy Emitted by the Atmosphere (1) 1) How much energy is emitted per unit area from the Earth? where σ is the Stefan Boltzmann constant and T E the temperature at which the Earth emits radiation.

88. 87 Climate modeling Again, to find the total amount of energy emitted by the Earth we need to multiply the flux with the area over which energy is emitted. Longwave radiation is emitted from the entire Earth surface and hence: Energy Emitted by the Atmosphere (2) 2) How much energy is emitted in total from the Earth?

89. 88 Climate modeling On average the energy absorbed and emitted by Earth have to balance, as otherwise the system would heat or cool indefinitely. We can calculate the temperature the Earth emits at by assuming a balance of incoming and outgoing energy: Earth’s Radiative Balance (1)

90. 89 Climate modeling Earth’s Radiative Balance (2) The world’s simplest climate model

91. 90 Climate modeling Global Energy Balance Summarized 342 W/m 2 235 W/m 2 107 W/m 2 Temperature Incoming solar radiation Reflected solar radiation Outgoing long wave radiation

92. Positive Attributes of Different Approaches to Seasonal Forecasting 2-Tiered Forecast Systems: -Relatively inexpensive computationally -Potentially more accurate SST data due to input from multiple sources -No drift of SST annual cycle on which anomalies are superimposed 1-Tiered Forecast Systems: -Potentially more accurate representation of physical interaction between ocean and atmosphere: Transient (waves) and time mean

93. Tier-Two models used for prediction of Indian Monsoon

94. Seasonal Prediction of the Indian Monsoon (SPIM)

95. Observed and simulated variation of all-India rainfall: 1985-2004 Note:(1988, 2001, 2002) – consistency among the models; 1994 all models failed Seasonal Prediction of the Indian Monsoon (SPIM) CC=0.39

96. 5-AGCM EM hindcast skill (21Yr) OBS SST-rainfall correlationModel SST-rainfall correlation Two-tier system was unable to predict ASM rainfall. TTS tends to yield positive SST-rainfall correlations in SM region that are at odds with observation (negative). Treating monsoon as a slave to prescribed SST results in the failure. Hindcast Skill is nearly Zero in ASM region Wang et al. 2005 Two-tier MME hindcast of summer Monsoon rainfall

97. Effect of Coupling on Simulated Indian Summer Monsoon correlations (%) with CPC GSOD 1980–2003 Coupled uncoupled un-Coupled (Taken from Dewitt)

98. Hindcast skill of CFS vs Simulation Skill of GFS ACC of Coupled model ACC of un-coupled model Chaudhari et al., (2013)

99. ISMR simulation by GFS and hindcast by CFS Chaudhari et al., (2013)

100. SST-Rainfall Correlation Coupled Un-coupled Observed Chaudhari et al., (2013)

101. SST-Rainfall correlation t different lag/leads Chaudhari et al., (2013)

102. Teleconnections with Nino3.4 Coupled Un-coupled Observed Chaudhari et al., (2013)

103. 1984-2005 0.36 Rajeevan et al., (2012)

104. Thank you