Forecasting Theory Types Examples
How Good Are Week Out Weather Forecasts? For forecasts greater than nine days out, weather forecasters do WORSE than the climate average forecast.
Why is there predictability at seasonal times scales? Even though there is no skill in weather forecasting at seasonal lead times, there is a skill in predicting anomalies of seasonal average of the weather climate anomalies Slowly changing conditions (at surface) : SST, snow/ice cover, soil wetness. Atm. Circulation Patterns Climate Prediction Skill
ENSO ENSO events are predictable Long-lasting Govern Teleconnection Patterns 1/3 of the land areas have predictable effect
The State-of-the Art Climate Prediction Effect of SST is detected by averaging over a month/season, etc Day-to-day fluctuations of daily mean temperature can be ~10C, seasonal anomalies ~1.5C Effects of the daily weather variability cancel themselves Circulation patterns associated with the SST anomaly, do not occur steadily throughout the season but rather have a tendency to set up more frequently than they would without the tropical SST anomaly Uncertainty comes from unpredictability of some weather events Probabilistic forecast is needed (not deterministic)
Forecast Methods Statistical use observations from past looking for repetitions of same patterns in the future
Forecast Methods Statistical use observations from past looking for repetitions of same patterns in the future Dynamical understand how the system (atmosphere, ocean) works, formulate equations describing that behavior, use them to forecast.
Forecast Methods Statistical use observations from past looking for repetitions of same patterns in the future Dynamical understand how the system (atmosphere, ocean) works, formulate equations describing that behavior, use them to forecast. - Analytical pen & paper
Forecast Methods Statistical use observations from past looking for repetitions of same patterns in the future Dynamical understand how the system (atmosphere, ocean) works, formulate equations describing that behavior, use them to forecast. - Analytical pen & paper - Numerical computers
Forecast Methods Statistical use observations from past looking for repetitions of same patterns in the future Dynamical understand how the system (atmosphere, ocean) works, formulate equations describing that behavior, use them to forecast. - Analytical pen & paper - Numerical computers Physical to-scale model
Statistical Forecasting
Statistical Forecasting
METHODOLOGY: Since winds (v) apparently lead currents (u), can we forecast Currents from winds u=u(v)? Let s try the following statistical model (one input model) u*(t)= a v(t+ ) where t=time, a=proportionality coefficient and = lag Task is to find the values of a and that minimize =<(u*-u)²>, where < > means average in time.
Two-input models of one and two variables A better and more reliable model can be built by using other times of v as additional predictand: u(t)= a * v(t+ ) + b * v(t+ ) where is a lag different from, such that it adds non-redundant information (if it is too close it will not add predictive skill). in the 2 nd term on the right hand side, v can be replaced by a 2 nd variable This is an equation for predicting 14C isotherm depth off CA coast from Tropical SST and off CA coast wind stress anomalies : H(t)= a * SST(t+ ) + b * τ(t+ )
Predicting 14C Isotherm Depth in CA Bite from NINO3 and TAUY
Cross-Correlation Coefficients Tauy and NINO3 lead 14C Isotherm Depth by 5 months
Cross-Correlation Coefficients Correlation coefficient between observed and predicted =.67
Statistical Significance Question: what s the probability for our results to be obtained by pure chance? - Generalized Method (e.g., Davis 1976 for correlation coefficients). - Monte Carlo Simulations (repeat your statistical calculation/estimation replacing your data with random data). Then, obtain significance levels and/or error bars.
Dynamical Forecasts 1. Know the physics of the system (how it behaves and why) 2. Describe it with mathematical formulations (conservation laws) 3. Define a) initial conditions b) boundary conditions (forcing) Air-sea wind Heat fluxes Currents, temps, salinity Bottom boundary condition 4. Solve equations based on initial conditions and forcing
Conservation Laws (momentum, energy, mass, heat, etc) CONCEPT: for any quantity (temperature, salt, mass, energy) inside a given volume of the system (ocean, atm, etc): Change of quantity = horizontal advection by currents + vertical advection by currents + vertical diffusion + horizontal diffusion + forcing (injection of that quantity from outside the system) + losses due to, e.g., friction
Example: analytical expression dt/dt = - u du/dx - w dt/dz + Q + d(k(dt/dz)/dz +d(m(dt)/dz) Change = hor. Adv.+ vert adv + forcing + vert diffusion + hor diff Solve for T forecast T(n+1)-T(n) /dt = (..) T(n+1) =T(n)+dt* ( ) Where n is time
INDIA Thailand Example 1: Numerical solution of sea level equation: 2004 Tsunami
PHYSICAL (to-scale) FORECASTS HYDROLAB: 7/26 Lab model (scale 1:100)
How Good Are the Forecasts?
NINO3.4 INDEX
CURRENT ENSO CONDITIONS
JULY 2010 ENSO FORECAST
Probabilistic ENSO Forecast (from July 2010) Season La Niña Neutral El Niño JAS 2010 80% 20% 0% ASO 2010 80% 20% 0% SON 2010 80% 19% 1% OND 2010 80% 19% 1% NDJ 2011 79% 20% 1% DJF 2011 76% 22% 2% JFM 2011 72% 25% 3% FMA 2011 65% 30% 5% MAM 2011 52% 38% 10% AMJ 2011 32% 50% 18%
DETERMENISTIC PRECIPITATION FORECAST (from July 2010)
PROBABILISTIC PRECIPITATION FORECAST (from July 2010)
Model-Observations Comparison
Observations (top) vs. Model Forecast (bottom) of Sea Surface Temperature Anomalies for Jan 1983
Data Assimilation = Method that imposes additional constrains to models requiring them to reproduce observations
Fire Forecast ForecastValidation Model Skill log acres burned (anomalies from long term average) Correlation
Example 2: Tidal dispersion at coastal location