Models – Weather - Climate · Examples of External Parameters that can be modified: 1. The...
Transcript of Models – Weather - Climate · Examples of External Parameters that can be modified: 1. The...
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Models – Weather - Climate
René D. Garreaud
Departement of GeophysicsUniversidad de Chilewww.dgf.uchile.cl/rene
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Pronóstico del Tiempo y Predicción Climática
Herramienta
Res
oluc
ión
Esp
acia
l [km
]
10.0
1.0
100.0
31 7
Tormentasde Invierno
Tormentasde Verano
Variabilidad intraestacionale interanual de Precip.
• Pronóstico Numérico del Tiempo + MOS
• Modelos climáticos estadísticos
• Extrapolación observaciones• Modelos de mesoescala y microescala
30 300
0.1
0.1
1000×1000
5000×5000
Cobertu ra es paci al [km
2]
100×100
10×10
0.5
Plazo de Previsión [días]
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My first toy modelA system of coupled, non-linear algebraic equations
X(t) = A·X(t-1) ·Y(t) + B·Z(t-1) + εx
Y(t)= C·X(t-1)·Y (t-1) + B·Z (t)+ εy
Z(t)= D·Z(t-1)·Y (t) + E·X(t-1) + εz
εx = εy = εz = 0
X, Y, Z: Time-dependent variablesPressure, winds, temperature, moisture,….
A, B, C, D: External parametersOrbital parameters, CO2 Concentration, SST (AGCM), Land cover
εx εy εz Random errorsSet to zero → Deterministic model
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My first toy model
X(t) = A·X(t-1) ·Y(t) + B·Z(t-1) + εx
Y(t)= C·X(t-1)·Y (t-1) + B·Z (t)+ εy
Z(t)= D·Z(t-1)·Y (t) + E·X(t-1) + εz
εx = εy = εz = 0
To run the model, we need:
• Initial conditions: X0, Y0, Z0
• The values of the External Parameters … they can vary on time
• A numerical algorithm to solve the equations
• A computer big enough
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ObsMod
Weather forecastModel predicts daily values
Climate PredictionModel does NOT predict daily valuesbut still gives reasonable climate state
(mean, variance, spectra, etc…)
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The Lorenz’s (butterfly) chaos effect
X0 = -0.502X0 = -0.501
A slight difference inthe initial conditions
Large differenceslater onNon-linear
equations
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Nevertheless, simulations after two-weeks are still “correct” in a climatic perspective and highly dependent upon external parameters → models can
be used to see how the climate changes as external parameters vary.
A=2
A=1
Two runs of the model, everything equal but parameter ANote the “Climate Change” related to change in A
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Examples of External Parametersthat can be modified:
1. The relatively long memory of tropical SST can be used to obtain an idea of the SST field in the next few months (e.g., El Niño conditions). Using this predicted SST field to force an AGCM, allows us climate outlooks one season ahead.
2. Changes in solar forcing (due to changes in sun-earth geometry) are very well known for the past and future (For instance, NH seasonality was more intense in the Holocene than today). Modification of this parameter allow us paleo-climate reconstructions (still need to prescribe other parameters in a consistent way: Ice cover, SST, etc.…hard!)
3. Changes in greenhouse gases concentration in the next decades gases give us some future climate scenarios.
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Atmospheric circulation is governed by fluid dynamics equation + ideal gas thermodynamics
gFpVkfdtVd
R
vvvr
+−∇−=×+ρ1ˆ
SfcConvRADP QQQSTVt
++=−∇⋅+∂∂ ω)(
v
0=∂∂+⋅∇
pV ωv
pRT
pgz −=∂
∂ )(
Momentum eqn.
Energy eqn.
Mass eqn.
Idea gas law
ECdt
dqv +−=
rr SEC
dtdq
+−+=
Water substanceeqns.
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¿¿¿Where is precipitation???
Water Vapor
Ice crystalCloud droplets
SnowRain droplets
Graupel/Hail
rcv EEC
dtdq
++−=
cccc KAEC
dtdq
−−−+=
rsrrccr FPPFEKA
dtdq
∝→−−+=
War
mclo
ud
Cold clouds
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Previous system is highly non-linear,with no simple analytic solution
.... We solve the system using numerical methods applied upon a three-dimensional grid
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∆ lat
∆ lon
∆ z
Global Models (GCM)
∆lat ~ ∆ lon ~ 1° - 3° ∆z ~ 1 km ∆t ~ minutes-hoursTop of atmosphere: 15-50 km
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Global Models (GCM)
PP/CP/CCCCGCM
C
P
P
Biosphere
CCCCESM
PPCCOGCM
PPPPAGCM
Land use
Land Ice
Sea Ice
SSTType
Com
plex
ity
1980-
1990-
2005-
A: Atmospheric Only; C: Coupled; O: Ocean; ESM: Earth-system models
External parameters: GHG, O3, aerosols concentration; solar forcing
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Regional Models (LAM, Mesoscale Models)
∆ z
∆ y
∆ x
Ly
Lx
Lz
∆x ~ ∆ y ~ 1-50 km ∆ z ~ 50-200 m ∆ t ~ secondsLx ~ L y ~ 100-5000 km Lz ~ 15 km
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Regional Models (LAM, MM)
Regional models gives us a lot more detail (including topographic effects) but they need to be “feeded” at their lateral boundaries by results from a GCM.
Main problem: Garbage in – Garbage out
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Once selected the domain and grid, the numerical integration uses finite differences in time and space
diabQxTu
tT
=∂∂
+∂∂
Numerial method(stable & efficient)
diab
it
iti
t
it
it Q
xTTu
tTT
=∆−
+∆− −+
−−+
11
111
Sub-grid processes must be parameterized, that is specified in term of large-scale variables
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Thus, a real atmospheric model has
DynamicalCore
Cloudmicrophysics
Boundary layerturbulence
RadiativeTransfer
Surfaceproceses
Convectiveclouds
Param. otrosprocesos SG
For instance, MM5 (LAM) has 220 programs, 50 directories and 55.000 code lines F77...Ufff!
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¿Pronóstico Numérico del Tiempo ?
Conocer la distribución espacial y temporalde las variables que caracterizan la atmósfera
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Lon (x)
Lat (
y)
. . . T wupEl
ev(z
)
Con todo esto se realiza la simulacionnumérica (∆t ~ 1-5 días)
Condiciones iniciales ( t0 )
Modelo
NuméricoCondiciones de
borde (LAM)
. . . T wup
Elev
(z)
Pronósticos
( t0+ ∆t )
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Modelos numéricos de pronóstico: ¿Maquinas versus humanos?
Salidas numéricas
. . . T wup
(Guidance) Mapas y otras formas graficas para el apoyo del pronóstico subjetivo realizado por un meteorólogo
Post-procesamiento estadístico (MOS, Perfect Prog, redes neuronales, etc.) permiten pronóstico objetivo
Pronóstico de variables meteorológicas(e.g., Tx, Precip.) para un lugar o región
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La resolución espacial determina que rasgos geomorfológicos y meteorológicos estarán
presentes en la simulación/pronóstico…aumento de res. Es caro
∆x = 5 km∆x = 0.1 km
∆x = 45 km∆x = 15 km
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Posibles fuentes de errores
1. Errores en las condiciones iniciales (o de borde).CI asimilan información, pero extrapolación dinámica es importante. Predictabilidad limitada a 5-7 días.
2. Errores en la parametrización de procesos sub-grilla
3. Errores derivados de falta de resolución espacial
4. Errores numéricos (mínimos)
Resultados deben ser validados para estimar errores aleatorios y corregir errores sistemáticos
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Validación de los pronósticos
Area precip. pronosticada
Area precip. observada
Punto de interes
y
x
¿Buen pronóstico? ¿Mal pronóstico?La perspectiva (local-espacial) lo define todo...
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La bondad del pronóstico es una medida objetiva de su capacidad de acertar estados futuros de la atmósfera:
Variables continuas: R2, ecm, sesgo, etc....
ecm
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En el caso de variables discretas (o variables continuas discretizadas) se emplean tablas de contingencia
Cada celda la frecuencia de ocurrencia de un estado i dado un pronóstico de estado j ( f {i/j} )
fNNpN
......
f44p4
f33p3
f23f22f21p2
f13f12f11p1
oN....o4o3e2o1
(Pronóstico perfecto: f {i/j} = 0 si i ≠j)
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Caso más simple y mas frecuente N=2
1006535
70D=60C=10Pron.
No-Lluvia
30B=5A=25Pron. Lluvia
No-LluviaLluvia
ObservaciónN=100
Climatología observada
Climatologíadel pronóstico
Hit-rate: (25+60)/100 85%False-alarm rate: 5/100 5%Missing rate: 10/100 10%
Muchos otros mas...Bias, TS, POD,...
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Sin embargo los índices anterioresNO dicen mucho del pronósticos por si solos...
La bondad del pronóstico se establece al comparar sus índices con los obtenidos con otras formas de estimar las condiciones futuras:
• Otros sistemas de pronósticos• Persistencia• Azar• Climatología
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Particular cuidado en pronóstico de eventos muy infrecuentes.
Nuestro pronóstico. HR=0.91 Pronóstico fijo. HR=0.95
100955
96915Pron.
No-Lluvia
440Pron. Lluvia
No-LluviaLluvia
ObservaciónN=100
100955
100955Pron.
No-Lluvia
000Pron. Lluvia
No-LluviaLluvia
ObservaciónN=100
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La expansión de la comunidad de meteorología operativa
Condiciones Iniciales y de Borde generadas por modelos globales (e.g. AVN) en tiempo real vía Internet
Códigos numéricos portables y eficientes (MM5, RAMS, WRF, etc…)
Modelos numéricos de pronóstico del tiempo de área limitada corriendo en forma operacional en múltiples instituciones:
• Servicios Met. Nacionales• Universidades• Centros regionales• Empresas privadas• Consultoras en meteorología
Internet provee además un medio de difundir los resultados de estos modelos.
Cluster y Super PC a precios accesibles
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La expansión de la comunidad de meteorología operativa
La creciente superposición entre los diversos actores de la comunidad meteorológica operativa no solo ocurre en el campo de la predicción numérica del tiempo, sino también en la colección y diseminación de observaciones meteorológicas.
Escenarios posibles frente a esta superposición:
♦ Generar una saludable colaboración, promoviendo por ejemplo sistemas de pronósticos basados en “Ensambles” y coordinando esfuerzos de investigación aplicada que no pueden ser ejectudados en forma individual
♦ Indiferencia y/o tensión entre los actores (publico/privado, tradicionales/emergentes). Superposición pasa a ser considerada invasión.
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Modelos numéricos de pronóstico¿Maquinas versus humanos?
Baars and Mass (2005) obtuvieron las siguientes conclusiones:
• En general, los pronósticos objetivos (MOS) han alcanzado y superado a los pronósticos subjetivos de temperaturas extremas y probabilidad de precipitación.
• Los mejores pronósticos objetivos emplean sistemas mas o menos sofisticados de MOS aplicados a las salidas de varios modelos numéricos (Consensus MOS, Weighted MOS, etc.)
• La calidad de los pronósticos objetivos decae en situaciones extremas (e.g., grandes cambios de temperatura), pues los MOS están calibrados para los valores medios.
• Los pronósticos subjetivos (guiados por salidas numéricas) continúan siendo mejores en el rango 0-24 horas, donde los meteorólogos pueden integrar en forma efectiva otras fuentes de información.
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¿Qué quieren los usuarios?(especialmente los que pagan)
Atmósfera – Meteorología - Clima
Modelos de Pronóstico Meteorológico (MPM)(T, p, q, V, Φ,R, H, LE,...)
Modelos intermedios congrado de complejidad variable
Variables Ambientales
Indices de ventilación, Probabilidad de heladas, potencial de incendio, caudales, etc...
Sectores Productivos (Agricultura-Forestal, Pesca, Energía,Agua, Minería, Transporte) y Sistemas de Protección Civil
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Modelos intermedios
• Post-procesamiento de resultados del MPN (e.g., horas de frío, índice de ventilación) y un escalamiento espacial hacia abajo (10×10 km → 1×1 km)
• Combinación MPN con información meteor.precedente (e.g., lluvias en el último mes para calculo de humedad del suelo) y/o información ambiental concurrente o precedente (e.g., índice actual de vegetación para determinar potencial de incendio).
• Enlace MPN con modelos adicionales (e.g., modelo de nieves, modelo de olas, modelos de evapotranspiración, etc.)
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Conclusiones I
• Es fundamental conservar y analizar el desempeño de los pronósticos en forma estadística. La bondad de un modelo es una medida relativa.
• El beneficio asociado a los pronósticos (y su valorización) depende de su desempeño, pero también de las acciones que se ejecutan a partir de ellos.
• La creciente disponibilidad de recursos para ejecutar modelos numéricos del tiempo contribuye a ampliar la comunidad operativa, con las oportunidades y desafíos que ello conlleva.
• Pronósticos objetivos (e.g., MOS) parecen destinados a superar a los pronósticos subjetivos en previsiones sobre un día.
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Conclusiones II
En consecuencia, las instituciones involucradas en meteorología operativa deberían re-orientar sus esfuerzos a:
• Desarrollo de sistemas objetivos basados en múltiples modelos numéricos (e.g., Ensemble MOS)
• Análisis y pronóstico subjetivo de corto plazo (0-24 horas), en especial en presencia de condiciones lejos de la climatología
• Desarrollo interdisciplinario de modelos “ambientales” intermedios que, basados en los resultados de los modelos numéricos del tiempo, permitan la predicción de variables especificas y de directo interes para sectores productivos