![Dynamical Prediction on weather scales in the monsoon region has
improved substantially
Fig. MME forecasts track based on different initial
conditions for the tropical cyclone HUDHUD, from NWP REPORT
ON CYCLONIC STORMS OVER THE NORTH INDIAN OCEAN DURING 2014, Kotal et al.,
NCMRWF rep., 2015
Total precipitation [mm/day] for (a) CMORPH over 28–29 July 2010 and (b)
ECMWF ensemble mean of the forecast initialized four days previously (July
24, 2010) for the same time period. White contour shows 20 mm/day.
ECMWF 15‐day forecast of the precipitation [mm/day] in the red rectangle
(Figure 1a) initialized on July (c) 22nd, and (d) 24th, 2010. Black dashed line
shows the ensemble mean. Colored shading depicts the probability of
precipitation rate based on the 51 ensemble members. Dark blue line
represents the observed CMORPH precipitation averaged for the same
Region (Webster et al., 2010, GRL)](https://image.slidesharecdn.com/event31-200205141810/75/Event-31-36-2048.jpg)
Event 31
- 1. The equations ofmotion for weather forecasting through climate change studies K. Ashok Centre for Earth, Ocean & Atmospheric Sciences University of Hyderabad ashokkarumuri@uohyd.ac.in
- 2. Introduction: Geophysical FluidDynamics • The effects of rotation and those of stratification Distinguish the GFD. • The rotation of the earth around its axis introduces Coriolis force, which adds a certain amount of rigidity. • Stratification, the other distinguishing attribute of geophysical fluid dynamics, arises because naturally occurring flows typically involve fluids of different densities (e.g., warm and cold air masses, fresh and saline waters). Here, the gravitational force is of great importance, for it tends to lower the heaviest fluid and to raise the lightest. Under equilibrium conditions, the fluid is stably stratified, Fluid motions, however, disturb this equilibrium. Small perturbations generate internal waves. • Large perturbations, especially those maintained over time, may cause mixing and convection. For example, the prevailing winds in our atmosphere are manifestations of the planetary convection driven by the pole-to-equator temperature difference
- 3. The start: equationsof motion: • Conservation of momentum (F=ma) Du Dt fv x Fx Dv Dt fu y Fy 0 p RT p x y z Hydrostatic balance (neglect vertical accelerations) • Conservation of mass (no thermonuclear reactions) d dt r u 0 u x v y p 0 = dp/dt = pressure velocity T dt u T dx v T dy ( T p RT pcp ) J cp • Conservation of energy (ditto) • Equation of state (a gas) p RT * For an ocean model, you have also an equation for salinity.
- 4. Prognostic/Diagnostic Equations Equations (1a),(1b), (3), and (4) are called prognostic equations because time changes in forecast variables (u, v, T, and q) are determined explicitly using dynamic forcing equations. In equations (2) and (5), the remaining variables ( w and z) are determined from the prognostic variables. Because they do not calculate time changes directly, they are known as diagnostic equations.
- 5. What is aModel? •Take the equations of fluid mechanics and thermodynamics that describe atmospheric processes. •Convert them to a form where they can be programmed into a large computer. •Solve them so that this software representation of the atmosphere evolves within the computer. •This is called a “model” of the atmosphere
- 6. Solve equations ona sphere Solve in the vertical Solve in the horizontal grid Spherical harmonics
- 7. Not just theatmosphere…
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- 10. Governing equations • Anexample of one momentum equation: 1-d wind accelerated by only the pressure gradient force x p Dt Du 1 Computers cannot analytically solve even this very simple equation!
- 11. Integration of theequations 1 1 1 2 k k k k ki i i i i U U U U U t x U U U t x Nonlinear advection
- 12. Weather Prediction byNumerical Process Lewis Fry Richardson 1922
- 13. Weather Prediction byNumerical Process Lewis Fry Richardson 1922 •Predicted: 145 mb/ 6 hrs •Observed: -1.0 mb / 6 hs ps t
- 14. In 1928, theGerman mathematicians Courant, Friedrichs, and Lewy systematically studied how to solve partial derivative equations by using finite differences and specified the constraints to comply with when performing discretization (Courant et al., 1928), the CFL criteria. In 1939, the Swede Carl Gustav Rossby showed that the absolute vorticity conservation equation provided a correct interpretation of the observed displacement of atmospheric centres of action (Rossby, 1939).
- 15. First Successful NumericalWeather Forecast: March 1950 • Grid over US • 24 hour, 48 hour forecast • 33 days to debug code and do the forecast • Led by J. Charney (far left) who figured out the quasi-geostrophic equations Tropical Weather Prediction is all together extremely challenging…a different level
- 16. Scales of processes/models •Jetstreams •High and low pressure centers •Troughs and ridges •Fronts •Thunderstorms •Convective complexes •Tropical storms •Land/sea breezes •Mountain/valley breezes •Downslope wind storms •Gap flows •Cold air damming •Nocturnal low-level jets •Lake-effect snow bands Synoptic MesoGlobal •Long waves •El Nino •Street-canyon flows •Channeling around buildings, wakes •Vertical transport on upwind and warm faces of buildings •Flow in subway tunnels Urban
- 17. How the ModelForecasts Time Temperature T now (observed) X X Model-calculated T changes X X X X
- 18. Integration of theequations 1 1 1 2 k k k k ki i i i i U U U U U t x U U U t x Choose time step based on expected wind speeds and grid spacing k i x t U Nonlinear advection Time step
- 19. Horizontal grid structures MM5and others WRF and others From Randall (1994)
- 20. Unstructured: Omega Model FromBoybeyi et al. (2001)
- 21. For example •The useof sigma coordinates, rather than pressure or height, avoids complications that arise when the pressure or height surfaces intersect the ground, especially in mountainous areas sigma coordinate is defined by = p/ps
- 22. Purpose of modelling •Forecastingweather •Extended & Seasonal prediction •Ocean weather •Climate change •Applications •Understanding of physical and dynamical mechanical Processes •Theoretical studies with simplified processes
- 23. Modelling Philosophy The MOSTimportant principle of modelling, and challenge is ..
- 24. Sources of modelerror • Numerics/numerical schemes • Physics (radiation, turbulence, moist processes) • Initial conditions - define the atmosphere’s current state…the starting point • Lateral boundary conditions - define the atmosphere’s state at domains’ edges • Lower boundary conditions – conditions at Earth’s surface
- 25. MM5: leapfrog (t)and 2nd-order centered (x) Runge-Kutta (t) and 6th-order centered (x)
- 26. “Nested” grids • Gridscan be telescoped, or nested, to zoom in on a small area Large grid-point spacing – say 90 km 30 km 10 km
- 27. Physical Process representations:Parameterizations • Parameterizations approximate the bulk effects of physical processes that are too small, too complex, or too poorly understood to be explicitly represented Bauer et al., Nature 2015 Physical process representations
- 28. Data Assimilation injectsobserved data sets intermittently in to evolving model forecast to constrain its evolution towards observations Figures from
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- 32. P Bauer etal. Nature 525, 47-55 (2015) doi:10.1038/nature14956 Key challenge areas for NWP in the future. • Advances in forecast skill will come from scientific and technological innovation in computing • The representation of physical processes in parameterizations, • Coupling of Earth-system components, • The use of observations with advanced data assimilation algorithms, and the consistent description of uncertainties through ensemble methods and how they interact across scales. • The ellipses show key phenomena relevant for NWP as a function of scales between 10-2 and 104 km resolved in numerical models and the modelled complexity of processes characterizing the small-scale flow up to the fully coupled Earth system. • The boxes represent scale- complexity regions where the most significant challenges for future predictive skill improvement exist. • The arrow highlights the importance of error propagation across resolution range and Earth-system components.
- 33. TROPICAL WEATHER PREDICTION •IS CHALLENGING OWING TO THE DIFFERENT DYNAMICS • FOR EXAMPLE, HUGE MERIDIONAL TEMPERATURE GRADIENTS PROVIDE THE ENERGY FOR MID-LATITUDE SYSTEMS. HUGE PRESSURE/TEMPERATURE GRADIENTS. SIMPLE PHYSICS • UNLIKE THIS, IN THE TRPOPICS, THE ENERGY HAS TO BE DIABATIC IN NATURE, MAINLY FROM CONVECTION • ~CLOUDS OF 1-10 KM HORIZONTAL SCALE PROVIUDE ENERGY TO DRIVE A 600 KM SIZED TROPICAL CYCLONE. • LACK OF OBSERVATIONS, RESOURCES, AND COMPUTING POWER.
- 34. Normal Conditions El Niño-SouthernOscillation, and its types Ashok et al., J. Geophys. Res., 2007; Ashok and Yamagata, Nature New & Views, 2009
- 35. Operational MME seasonalprediction of the ENSOs, types and impacts Jeong et al., Clim. Dyn. JGR (2012) As the Chief of operations, introduced operational 6-month lead MME seasonal prediction at the APCC for ENSO types as well as climate (Jeong et al., JGR 2012). Also introduced a new MME method, named as “Climate Filter” based multi-model MME (Lee et al., JGR 2011), and a global drought monitoring product (Sohn et al., Int. J. Climatol. 2011)
- 36. Dynamical Prediction onweather scales in the monsoon region has improved substantially Fig. MME forecasts track based on different initial conditions for the tropical cyclone HUDHUD, from NWP REPORT ON CYCLONIC STORMS OVER THE NORTH INDIAN OCEAN DURING 2014, Kotal et al., NCMRWF rep., 2015 Total precipitation [mm/day] for (a) CMORPH over 28–29 July 2010 and (b) ECMWF ensemble mean of the forecast initialized four days previously (July 24, 2010) for the same time period. White contour shows 20 mm/day. ECMWF 15‐day forecast of the precipitation [mm/day] in the red rectangle (Figure 1a) initialized on July (c) 22nd, and (d) 24th, 2010. Black dashed line shows the ensemble mean. Colored shading depicts the probability of precipitation rate based on the 51 ensemble members. Dark blue line represents the observed CMORPH precipitation averaged for the same Region (Webster et al., 2010, GRL)
- 37. Dynamicalweather prediction for theIndian sub-continent has improved substantially Fig. MME forecasts track based on different initial conditions for the tropical cyclone HUDHUD, from NWP REPORT ON CYCLONIC STORMS OVER THE NORTH INDIAN OCEAN DURING 2014, Kotal et al., NCMRWF rep., 2015
- 38. Diagnosis methods • Statisticshelp as powerful data reduction methods - linear and non- linear (e.g. linear regression, EOF, SOM, etc.). • Graphics/Math softwares – GrADs, Ferret, MATLAB, NCL, IDL, Vis5D, etc.
- 39. 44 JJA Feb IC0.50 MAR IC 0.42 Apr IC 0.25 May IC 0.24 • Feb IC exhibits maximum skill at seasonal time scales viz. 0.55 for JJAS and 0.5 for JJA. • This translates to the spatial pattern as well, with Feb IC exhibiting the pattern reasonably. Courtesy: Suryachandra Rao, IITM Hindcast seasonal prediction correlation skills for summer monsoon rainfall (1983- 2010)
- 40. Aerosols affecting theClimate variability… Fadnavis et al. Climate Dynamics, (2017) TOMS Aerosol index (1978 - 2005) MISR AOD 2000 - 2010 Climatology El Niño years ECHAM5-HAMMOZ TOMS AI, and MISR AOD averaged for the April and May months show relatively high AOD loading can be clearly visible over the IGP. The ECHAM5-HAMMOZ model could reproduce higher than climatology during El-Nino over the IGP. Distribution of April-May average (a) TOMS aerosols index (AI) climatology 1978-2005, (b) TOMS aerosols index during El Niño years. MISR aerosols optical depth (AOD), (c) climatology (2000-2010) (d) El Niño years, ECHAM5- HAMMOZ simulated AOD obtained from (e) CTR_aeron (f) ElNiño_aero experiments
- 41. Aerosol impact onprecipitation Climatology El Niño El Nino producing less precipitation is captured by the model Distribution of mean seasonal mean precipitation (mm/day) from (a) CTR_aero (b) ElNiño_aero. Aerosol- induced changes in seasonal mean precipitation as obtained from (c) difference between CTR_aero and CTR_aeroOFF (d) difference between ElNiño _aero and ElNiño _aeroOFF experiments. Inclusion of aerosols in the model experiment reduces the severity of drought during El Niño Fadnavis et al. Climate Dynamics, (2017)
- 42. 47 (a) 101-year runningmean anomalies of ISMR (mm/day); The MWP & LIA period are shown in red & blue boxes, respectively. (b) Linear trend lines of the area-averaged ISMR during LM, as simulated by the nine PMIP3 models. • A statistically significant (at 0.10 levels) but the moderate decreasing trend in area-averaged ISMR in four models, and a weaker decreasing trend in four more models throughout the LM, in agreement with findings from several proxy records. • A wet and warm Indian monsoon during MWP, and a cool and dry LIA. Tejavath et al., 2018
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- 44. Nino3 SST Precipitation (5N-35N; 65E-95E) Laggedcorrelation between ISMR and Nino3 SST in the preceding/following months (Swapna et al., BAMS, 2015) ENSO-Monsoon relationship Indian (land + ocean) Precipitation IITM ESM: IITM contributing to the CMIP6 with an improved version. Improved Monsoon-ENSO links are crucial o climate scales.
- 45. - A combinationof the BoB warming, a Mega El Niño, and unplanned development Images from the internet Diagnosis of the Chennai extreme Rainfall event, Dec. 2015: A perfect Extreme event Boyaj et al.; Clim. Dyn. (2017)
- 46. The extreme rainfallevent in Chennai, Dec 2015 Boyaj et al., Climate Dynamics, (2017) Daily accumulated rainfall (mm/day) from the TRMM The Mega El Niño, Dec 2015 SSTA (°C) • Did the Mega El Niño and the BoB warming trend contribute to the extreme Chennai rainfall event? • Our experiments with WRF model (30 km) answer this query. Time series area average (85E to 95E, 80N to 15N) of BoB SST anomalies
- 47. Coupling atmospheric models withspecial-application models • Transport and diffusion models • Sound-propagation models • Ocean wave models • Ocean circulation models • Parachute-drift models
- 48. Acknowledgments of sourceinformation • Fundamentals of Numerical Weather Prediction..Jean Coffier • Geophysical Fluid Dynamics: Cushman et al. • Dynamic Meteorology.. Holton • Introduction to Theoretical Meteorology.. Hess • Numerical weather and Climate Prediction..T.T. Warner • Research Papers • Drs. Suraychandra Rao, Pattanaik, Sahai, etc. • Internet material: L. Bengtson, M. Cresswell, Warner, Inez Fung, Aaron Donohoe, etc.