# Forecasting. Theory Types Examples

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1 Forecasting Theory Types Examples

2 How Good Are Week Out Weather Forecasts? For forecasts greater than nine days out, weather forecasters do WORSE than the climate average forecast.

3 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

4 ENSO ENSO events are predictable Long-lasting Govern Teleconnection Patterns 1/3 of the land areas have predictable effect

5 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)

6 Uncertainties of Climate Prediction Some processes and feedbacks between different parts of the Earth are not fully understood (effect of clouds) Lack of some observations (aerosols) Uncertainties in external forcing (how much pollution humans will be adding to the atmosphere in the future)

7 Forecast Methods Statistical use observations from past looking for repetitions of same patterns in the future

8 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.

9 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

10 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

11 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

12 Statistical Forecasting

13 Statistical Forecasting

14 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.

15 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+ )

16 Predicting 14C Isotherm Depth in CA Bite from NINO3 and TAUY

17 Cross-Correlation Coefficients Tauy and NINO3 lead 14C Isotherm Depth by 5 months

18 Cross-Correlation Coefficients Correlation coefficient between observed and predicted =.67

19 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.

20 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

21 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

22 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

23 INDIA Thailand Example 1: Numerical solution of sea level equation: 2004 Tsunami

24 PHYSICAL (to-scale) FORECASTS HYDROLAB: 7/26 Lab model (scale 1:100)

25 How Good Are the Forecasts?

26

27 NINO3.4 INDEX

28 July 2010 ENSO CONDITIONS

29 JULY 2010 ENSO FORECAST

30 Probabilistic ENSO Forecast (from July 2010) Season La Niña Neutral El Niño JAS % 20% 0% ASO % 20% 0% SON % 19% 1% OND % 19% 1% NDJ % 20% 1% DJF % 22% 2% JFM % 25% 3% FMA % 30% 5% MAM % 38% 10% AMJ % 50% 18%

31 DETERMENISTIC PRECIPITATION FORECAST (from July 2010)

32 PROBABILISTIC PRECIPITATION FORECAST (from July 2010)

33 CURRENT ENSO CONDITIONS PREDICTIONS Forecast ensembles consist of 40 members from initial a period of 10 days

34 For the June-August season the probabilities for La Nina, neutral and El Nino conditions are estimated at 9%, 84% and 7%

35 IRI Probabilistic ENSO Prediction for NINO3.4 Region Made in Jun 2011 Season La Niña Neutral El Niño JJA % 84% 7% JAS % 71% 15% ASO % 71% 15% SON % 70% 15% OND % 70% 15% NDJ % 69% 15% DJF % 69% 15% JFM % 69% 15% FMA % 68% 16% MAM % 66% 17%

36 Temperature outlook from June 2011

37 Precipitation outlook from June 2011

38 Model-Observations Comparison

39 Observations (top) vs. Model Forecast (bottom) of Sea Surface Temperature Anomalies for Jan 1983

40 Data Assimilation = Method that imposes additional constrains to models requiring them to reproduce observations

41 Fire Forecast ForecastValidation Model Skill log acres burned (anomalies from long term average) Correlation

42 Example 2: Tidal dispersion at coastal location

43 El Nino Modeling Using STELLA

44 El Nino

45 El Nino In the Tropics, El Niño episodes are associated with increased rainfall across the east-central and eastern Pacific and with drier than normal conditions over northern Australia, Indonesia and the Philippines

46 La Nina

47 La Nina La Nina usually weaker than El Nino Global La Nina Climate is less understood

48 NINO3 SST Anomalies

49 El Nino

50 La Nina

51

52 Recharge Oscillator Theory Four phases of the recharge oscillation: (a) the warm phase, (b) the warm to cold transition phase, (c) the cold phase, and (d) the cold to warm transition phase. The rectangular box represents the equatorial Pacific basin, the elliptical circle represents the SST anomaly, the thin and filled arrows represent wind stress anomaly associated with the SST anomaly, and the thick unfilled arrows represent the recharge/discharge of equatorial heat content.

53 Ekman Pumping/Suction Ekman pumping along the equator. (a) shows a plan view of the prevailing surface wind and resulting water transport in the ocean's Ekman layer. (b) is a corresponding cross section, showing the upwelling and resulting SST anomalies.

54 Recharge Oscillator Model

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