**2. The limitations of empirical models and the imperative for a dynamical model basis for seasonal forecasting**

Empirical models (or 'statistical models') are currently used by many meteorological services for seasonal climate outlooks. These models are based on empirical relationships, usually between ENSO based indices ('the predictors') and variables such as local rainfall and temperature ('the predictands'). Using current observed values of ENSO indices these past relationships can be used to create forecasts [13].

A warming of the climate system due to greenhouse gas forcing is predicted by theory, demonstrated by numerical predictions and has been observed over the course of the past century [14]. While the empirical relationships between climate predictors and predictands such as rainfall may be robust, in a warming climate, environmental indicators used as predictors are now frequently outside of the range of historical records, meaning that relationships are being assumed for events which do not have an historical analogue. In general, empirical models cannot reliably account for aspects of climate variability and change that are not represented in the historical record. Empirical forecasting usually depends on the assumption of stationary relationships between predictors and predictands. This also renders such schemes susceptible to periodic changes in these relationships due to decadal timescale variability.

For example, outlooks for tropical cyclone (TC) activity in the Australian region are based on a regression model using values indices representing major modes of variability in the ocean. The 2010-11 TC season featured to a very strong La Niña event with an unusually hot Indian Ocean, an event without historical precedent. In this case the statistical models significantly over-predicted the number of TCs that occurred in the Australian region. Analysis shows that the environmental indicators used for tropical cyclone seasonal outlooks for the Australian region in 2010-11 and 2011-12 are outliers in the predictor phase space, in other words, outside of the range of variability for which the model was tested and built.

Managing Climate Risk with Seasonal Forecasts 563

determine a global estimate of the state of the ocean and atmosphere based on the combination of available observations and using numerical methods based on a mix of physical and statistical relationships to infer the state of regions not subject to direct observation. The objective of the assimilation process is placing constraints on the observations to ensure they present a physically plausible set of initial conditions for the

A number of dynamical models are run at operational meteorological centres around the world. We briefly describe the main components here with reference to the model used operationally at the Australian Bureau of Meteorology for ocean temperature forecasts. The first component is an ocean data assimilation system, which provides an estimate of the state of the upper ocean based on an analysis of ocean observations. The observations of the ocean come from a variety of sources including satellite observations of sea surface temperature and sea level height, fixed, drifting and profiling buoys (such as the TOGA-TAO array which provides real-time observations of the region of the Pacific Ocean central

This ocean assimilation system initialises an ocean model though a complex process which attempts to bring the model into a state consistent with the oceanic observations but also such that it is internally balanced to minimise so called 'initialisation shock'. Ocean model resolution for the Bureau of Meteorology POAMA (Predictive Ocean Atmosphere Model for Australia) [17] is 2 degrees in longitude with a latitudinal resolution telescoping from 0.5 degrees near the equator to 1.5 degrees near the poles. The model resolves 25 vertical levels. Specialised coupling software is used to transmit surface fluxes of heat and momentum between the ocean model and an atmospheric model. The POAMA atmospheric model has a spherical harmonic horizontal structure with triangular truncation at wave number 47 (grid cells of roughly 250km by 250km when transformed) and 17 pressure levels. The atmospheric model typically has its own assimilation system to ingest data from available observations of meteorological parameters including wind, pressure and temperature. Coupled assimilation, in which the ocean and atmosphere are initialised together to reduce

Processes with a spatial scale smaller than the model grid scale are 'parameterised', which means a statistical or process-based model is used to represent the average effect of this process on the sub-grid scale. Design and configuration of sub-grid scale processes is a specialised and active area of research, with current activity focussed on the use of

Seasonal climate prediction is inherently probabilistic because the evolution of the climate system is highly sensitive to initial conditions. Small difference or 'errors' in the description of the initial climate state grow with time leading to very different forecast outcomes. To estimate the range of physically plausible outcomes, GCMs are typically run as an ensemble, in which a number of simulations are performed with slightly different initial conditions. The initial conditions are perturbed to realistically sample the plausible range of initial

stochastic models to better capture the uncertainty of the sub-grid processes.

ocean-atmosphere simulation.

to ENSO) and observations taken from ships.

initialisation shock is an area of current research.

climate states.

**Figure 3.** Time series for an Indian Ocean based climate index showing a trend. Such trends may reduce the efficacy of empirical prediction schemes. (Source: KNMI Climate Explorer: http://climexp.knmi.nl/).

Inter-annual variability in the intensity and distribution of tropical cyclones is large, and presently greater than any trends that are ascribable to climate change. However climate change impacts our ability to make skilful predictions of tropical cyclone activity using empirical models, because in the warming environment predictors such as SSTs now frequently lie outside of the range of past variability. Improved empirical methods can be developed to adjust for this, by incorporating trends and by treating predictors that lie outside the observed range of variability more cautiously [15]. However it is widely considered that dynamical models provide the best prospects for improved seasonal forecasting in the future, either through providing long range forecasts of environments favorable to cyclo-genesis, or through high resolution models that can provide an estimate of the number of cyclones expected to form.

#### **2.1. Seasonal forecasting with dynamical models**

An alternative paradigm for seasonal prediction is the use of coupled ocean-atmosphere General Circulation Models ('coupled models' or GCMs). State of the art coupled models consist of a physically based model of the ocean, usually solved using a grid based scheme, coupled to a physically based atmospheric model, often solved using a spectral spatial discretisation [16]. GCMs solve a set of dynamical equations ('the primitive equations') to project the current analysed state of the ocean-atmosphere system into the future. The term 'analysed' here is used quite deliberately to describe methods used to determine a global estimate of the state of the ocean and atmosphere based on the combination of available observations and using numerical methods based on a mix of physical and statistical relationships to infer the state of regions not subject to direct observation. The objective of the assimilation process is placing constraints on the observations to ensure they present a physically plausible set of initial conditions for the ocean-atmosphere simulation.

562 Risk Management – Current Issues and Challenges

built.

http://climexp.knmi.nl/).

of the number of cyclones expected to form.

**2.1. Seasonal forecasting with dynamical models** 

For example, outlooks for tropical cyclone (TC) activity in the Australian region are based on a regression model using values indices representing major modes of variability in the ocean. The 2010-11 TC season featured to a very strong La Niña event with an unusually hot Indian Ocean, an event without historical precedent. In this case the statistical models significantly over-predicted the number of TCs that occurred in the Australian region. Analysis shows that the environmental indicators used for tropical cyclone seasonal outlooks for the Australian region in 2010-11 and 2011-12 are outliers in the predictor phase space, in other words, outside of the range of variability for which the model was tested and

**Figure 3.** Time series for an Indian Ocean based climate index showing a trend. Such trends may

Inter-annual variability in the intensity and distribution of tropical cyclones is large, and presently greater than any trends that are ascribable to climate change. However climate change impacts our ability to make skilful predictions of tropical cyclone activity using empirical models, because in the warming environment predictors such as SSTs now frequently lie outside of the range of past variability. Improved empirical methods can be developed to adjust for this, by incorporating trends and by treating predictors that lie outside the observed range of variability more cautiously [15]. However it is widely considered that dynamical models provide the best prospects for improved seasonal forecasting in the future, either through providing long range forecasts of environments favorable to cyclo-genesis, or through high resolution models that can provide an estimate

An alternative paradigm for seasonal prediction is the use of coupled ocean-atmosphere General Circulation Models ('coupled models' or GCMs). State of the art coupled models consist of a physically based model of the ocean, usually solved using a grid based scheme, coupled to a physically based atmospheric model, often solved using a spectral spatial discretisation [16]. GCMs solve a set of dynamical equations ('the primitive equations') to project the current analysed state of the ocean-atmosphere system into the future. The term 'analysed' here is used quite deliberately to describe methods used to

reduce the efficacy of empirical prediction schemes. (Source: KNMI Climate Explorer:

A number of dynamical models are run at operational meteorological centres around the world. We briefly describe the main components here with reference to the model used operationally at the Australian Bureau of Meteorology for ocean temperature forecasts. The first component is an ocean data assimilation system, which provides an estimate of the state of the upper ocean based on an analysis of ocean observations. The observations of the ocean come from a variety of sources including satellite observations of sea surface temperature and sea level height, fixed, drifting and profiling buoys (such as the TOGA-TAO array which provides real-time observations of the region of the Pacific Ocean central to ENSO) and observations taken from ships.

This ocean assimilation system initialises an ocean model though a complex process which attempts to bring the model into a state consistent with the oceanic observations but also such that it is internally balanced to minimise so called 'initialisation shock'. Ocean model resolution for the Bureau of Meteorology POAMA (Predictive Ocean Atmosphere Model for Australia) [17] is 2 degrees in longitude with a latitudinal resolution telescoping from 0.5 degrees near the equator to 1.5 degrees near the poles. The model resolves 25 vertical levels. Specialised coupling software is used to transmit surface fluxes of heat and momentum between the ocean model and an atmospheric model. The POAMA atmospheric model has a spherical harmonic horizontal structure with triangular truncation at wave number 47 (grid cells of roughly 250km by 250km when transformed) and 17 pressure levels. The atmospheric model typically has its own assimilation system to ingest data from available observations of meteorological parameters including wind, pressure and temperature. Coupled assimilation, in which the ocean and atmosphere are initialised together to reduce initialisation shock is an area of current research.

Processes with a spatial scale smaller than the model grid scale are 'parameterised', which means a statistical or process-based model is used to represent the average effect of this process on the sub-grid scale. Design and configuration of sub-grid scale processes is a specialised and active area of research, with current activity focussed on the use of stochastic models to better capture the uncertainty of the sub-grid processes.

Seasonal climate prediction is inherently probabilistic because the evolution of the climate system is highly sensitive to initial conditions. Small difference or 'errors' in the description of the initial climate state grow with time leading to very different forecast outcomes. To estimate the range of physically plausible outcomes, GCMs are typically run as an ensemble, in which a number of simulations are performed with slightly different initial conditions. The initial conditions are perturbed to realistically sample the plausible range of initial climate states.

Ensemble strategies in theory allow for better estimation of the probability of extreme, or less likely events. The nonlinear nature of the coupled ocean-atmosphere system means that these probabilities may not be well estimated from a single 'best guess' deterministic forecast. Using simple decision models which will be discussed in more detail below, Palmer [18] demonstrated that the economic value of ensemble forecasts is greater than that of individual models or simple ensemble means.

Managing Climate Risk with Seasonal Forecasts 565

**Figure 4.** Retrospective forecasts of mean seasonal rainfall for the Murray Darling Basis produced using the POAMA 1.5 CGCM for 1997. Upper) Time series of the model ensemble rainfall anomaly (mm/day), Middle) Probability forecast derived from the number of ensemble members lying above the model median, Lower) Observed seasonal rainfall anomaly (mm/day), where E denotes the occurrence of the above-median event.

hard limits on our ability to make deterministic predictions of nonlinear systems. The simple fact that we do not have infinite precision means that instabilities on scales smaller than the smallest resolved model scale inevitably grow and affect the larger scale until no predictive skill remains [20]. The 'saturation time' after which the system is effectively

The second major category of prediction uncertainty is the sparseness and imprecision of earth system observations. As discussed above, the analysed state of the atmosphere and ocean is necessarily different from its actual state, and as such model projections are projecting an imperfect estimate of the initial state forward in time. As such even with a perfect physical model, predictions would be imperfect. This source of error interacts with the first, because instabilities growing from initial conditions that are not present in nature may produce possible future states that are inconsistent with actual potential future states. Ensemble forecasting allows this initial condition uncertainty to be estimated and quantified by sampling the space of plausible initial conditions and projecting this sample forward in

unpredictable is longer for the ocean than the atmosphere.

Because basic physics does not change under global warming, dynamical models are less compromised by climate change than statistical models. GCMs explicitly take into account climate processes that are important for seasonal climate prediction such as equatorial oceanic waves and atmospheric convection driven by ocean temperatures and are not constrained by what has occurred in the past. GCMs implicitly include the effects of a changing climate whatever its character or cause and can predict outcomes not seen previously.
