Intro to NWP numerical weather prediction Compiled by Henrik Vedel Center for Meteorological Models (CMM), Research and development department, Danish Meteorological Institute (DMI) Weather Prediction by Numerical Process Lewis Fry Richardson, Cambridge University Press, 1922 Fundamental equations Newton's second law Conservation of mass Equation of state for ideal gases Conservation of energy Conservation of water mass Effects of radiation, condensation, turbulence, surface friction, lower boundary conditions, etc. Discretization and solution by finite differences Kopieret fra ”Atmospheric Data Analysis”, R. Daley, Cambridge Univ. Press Richardson estimated 64000 people would be necessary for doing global NWP in a ”forecast factory”. For various reasons his test, for part of Europe, failed, with huge deviations between forecast and observations. • In 1950 NWP was done again, for the US using a real computer, taking about 24 h to make a 24 h forecast. • Due to more and better observations, faster computer, and better model physics, this time with success. • One reason for the improvement in observations was World War II, where knowledge about current and future weather was in many situation crucial to the planning of military actions. Fundamental equations Newton's second law (3 equations for 3D vind) Conservation of mass (continuity equation) Equation of state for ideal gases (p, rho, T relation) Conservation of energy (first law of thermo dynamics) Conservation of water mass Effects of radiation, condensation, turbulence, surface friction, lower boundary conditions, etc. By analysing the equations with atmospheric motions on the Earth in mind simplifications can be made. Some of these divide NWP models into categories. Momentum equations See ”An introduction to Dynamical Meteorology”, J. R. Holton, Elsevier Press Momentum equations See ”An introduction to Dynamical Meteorology”, J. R. Holton, Elsevier Press Most NWP models are based on the so-called ”primitive equations”, describing the atmospheric flow under the assumption the vertical flow is much slower than the horisontal, and under the assumption the height of the atmosphere simulated is small compared to the radius of the Earth. The primitive equations were first written down by Vilhelm Bjerknes, before Richardson had his go on a numerical solution. Example of primitive equations (for a system with pressure as vertical coordinate, catesian tangent plane in the horisontal, and neglecting curvature of Earth. Geostrophic wind equations Hydrostatic balance Continuity equation (mass conservation), relating horisontal divergence to vertical motions under the hydrostatic approximation Conservation of energy In addition an equation for conservation of water mass and equation of state Hence the main variables are 2D horisontal wind, temeperature, water vapour NWP model coordinate systems It varies from model to model, in each case care must be taken to ensure proper transformation between coordinate systems when trying to estimate a property based on NWP data. In general: A NWP model space is spherical or flat (LAM) Typically g, the graviational acceleration is a fixed constant. The height of the model surface is typically the geometric height wrt. mean sea level (geoid), when determining heights further up, it is typically the geopotential height increment above the surface, derived from pressure, density and the hydrostatic approximation, delta_p = -g rho delta_z , which is added to the surface height. The horisontal coordinates differ from model to model, typically being some type of lat-lon-grid in regional models, to spherical harmonics and more sofisticated grids in global models. Some models are run in grid space, some in spectral space. In most current models the vertical coordinate is tied to pressure, but is not pressure itself, most common are, Both have the benefit of being ”terrain following”, the coordinate being 1 at the surface, which simplifies the equations to solve in the lower atmosphere. The latter has constant pressure surfaces in the upper atmosphere, which among other things benefits the use of important satellite data. In some of the newer, non-hydrostatic, models the vertical coordinate is height Parametrisations • Operational NWP is mainly done on with horisontal gridsizes of the order 1 to 50 km. • Higher resolution enables more phenomena to resolved explicitly by the model. • But at any resolution, many processes occur on too small scale, or are simply too complex, to be explicitly included in the model. • Convective clouds have sizes of about 1 km, and are currently not resolved properly in operational NWP. • Clouds droplet formation occur on molecular scale, is not resolved, and far from understood in detail. Similarly the transfer of solar radiation is related to cloud microphisics. Interactions with the ground, related soil type, vegetation type, soil moisture and resulting evaporation are parametrised. When the horisontal resolution is increased, to order few km scale, we expect the hydrostatic approximation to become increasingly invalid. Hydrostatic NWP models cannot model the formation of individual convective systems, even the big ones. They are not good at modeling the airflow in regions with strong orography. They do not model gravity waves well at all, which can be of importance sometimes on even larger scales. •(Figure from Arakawa, presentation at workshop on Non-hydrostatic Modelling 8-10 Nov., 2010 ECWMF) Parameterizations Land surface Cloud microphysics Turbulent diffusion and interactions with surface Orographic drag Radiative transfer From J. Knievel In NWP ”language” processes that are resolved are often referred to as ”dynamics”, whereas processes not explicitly resolved are referred to as ”physics”. The ”physics” is in general ”tuned” for the model to perform the best in the area of interest. For this reason the NWP models of different met offices or universities can perform quite differently in different areas, without it being a real model error . Sometimes even for the same model, that is just tuned differently. It is important to have this in mind, when using results from different models or from different institutions for a specific area. MENU Ingredients of a numerical weather prediction system Observations Data assimilation system provide ”Analysis” (=initial conditions) Boundary values from external model Numerical weather prediction model Old model state Combined and done on a very powerfull computer Computer generated forecasts Forecasts by forecasters From NN Examples of HIRLAM (high resolution limited area model) run at DMI Example: HIRLAM S03/SKA details HIRLAM = High Resolution Limited Area Model Boundary conditions = ECMWF global model Horizontal grid resolution = 0.03° (approx 3 km) Vertical layers = 65 Grid points = 978 * 818 * 65 Approximately 8 variables Forecast length=54h, time step=90s Runs on 50 nodes (700 cores) using MPI parallelization; asynchronous I/O on 8 cores Much of the progress in NWP skill is due to faster computers enabling us to increase resolution, improve the data assimilation systems, improve the representation of physical processes. In addition the observing system is gradually improving, with more and novel types of observations. Global models are typically run 2 – 4 times a day, with forecasts out to about 15 days. Higher resolution, local area models (LAMs) are run 4 to 24 times a day, with forecasts typically in the range of 12 hours to several days. About non hydrostatic NWP Idealised test of N-H versus H NWP model Aladin From a presentation by Jan Masek Slovak HydroMeteorological Institute (28th EWGLAM meeting 2006) Very high resolution Test of N-H model, by run at double resolution. OK Test of N-H model, by run at double resolution. OK Now at 1 km resolution Findings in idealised tests From Jan Masek Some examples from DMI More realistic regarding a focus on real weather phenomena Less easy to conclude from.. Piteraq i Tasiilaq Feb. 6 1970 See Emilie Harmansson, Vejret 126, 2011. Thanks also to Niels Voetmann •Night time radiation results in colder air near surface. In steep orography the denser air slides toward lower levels, accelerating if it continues to be denser. •Hypothesis that N-H NWP is better to model this than hydrostatic NWP because of better handling of vertical dynamics and of orografic forcing. •If air mass moves in an area channeling the air, and into a low pressure area that can “absorb” the air, the wind speed is further increased. •Possibly gravity waves also strengthens the phenomon (similar in foen situations). • NH Arome versus H Aladin, rated by Meteo France forecasters • (from Benard, Meteo France, at workshop 8-10 Nov, 2010, ECMWF) Hydrostatic versus non-hydrostatic •The naming ”non-hydrostatic” is confusing to non-experts. Non-hydrostatic models do not miss something. It is the other way around! •In N-H models one includes a vertical acceleration term in the dynamic equations. In hydrostatic models this term is replaced by the simplifying assumption of hydrostatic balance (+inclusion of extra parametrisations). •On large scales, many km, the differences are in general not important. Running a hydrostatic model can be preferable – as it leaves cpu for other calculations. •On smaller scales, order one kilometer, differences become marked, N-H is superior. •On scales in between the situation is currently more complicated. If orographic forcing or gravity waves are of importance, N-H models have benefits. But in other cases, more typicical of the Danish area, the skill of other components of the NWP system (parametrisations, data assimilation, etc.) of importance to the particular weather type can be more important than non-hydrostatic versus hydrostatic. Verification • It is extremely important to monitor and to verify model performance. Both in order to improve models, and in order to choose between models for forecasting this and that. Different models and model setups have different skils – it is not one model always being better than the rest. • Divided into ”objective” and ”subjective” verification. • SUBJECTIVE: A forecaster, or other expert, compare by eye model output to observations or fields derived from observations. • OBJECTIVE: Traditionally two methods are used 1. Point comparision of model to observations. Typically done for 2mT, 2mRH, 10 m wind, and against radiosonde observations of wind, temperature and humidity at select pressure levels. Can in principle be done for any type of meteorological observation. Common is to derive bias and standard deviations. In case of precipitation, slightly more complex methods are used. 2. Model fields comparisons, between a forecast field and the ”analysis” valid at the same time. The analysis is the initial condition field from which an NWP run is started, and represents the current state of the atmosphere better than the forecasts. (or..) Example: Mslp, 2mT and 10m wind as function of forecast length over a month long period for 4 different models Example: 10m wind as function of day of month during one month, for 5 different models. Monitoring example: Meteogram for one location comparing 48 hour forecasts of 2mRH, 2mT, 10m wind direction and speed, and mslp. Monitoring example: Average 2mT and 10m wind speed for one month as function of time of day and forecast length. For 7 models started the same time very day. HIRLAM prediction case of EXTREME PRECIPITATION Forecasted 100 mm Observed 100 mm To improve forecasts: Improve resolution, increase forecast frequency, include extra observations to benefit the extra forecast cycles. To improve results from increased NWP resolution, observations with higher spatial density are needed. To improve results from higher NWP cycling rate (e.g. hourly instead of 6 hourly) more frequent observations are needed. The “traditional” meteorological observing system is not built for high resolution, rapid update cycling meso scale NWP. There is a particular lack of high resolution, rapid update observations related to humidity and precipitation in most current operational NWP setups. • • The purpose of the NWP nowcasting is to predict important weather phenomena that has low predictability because they occur on small scales in time and space, leaving them very difficult to predict properly with traditional NWP setups. Examples of importance to DMI/Denmark are: – Convective, heavy, local precipitation (risk of floodings, risk of waste water overflow). – Road temperatures, humidity, precip., cloud cover (e.g. slippery road forecasts, used by road authorities when planning salting etc.) – Short term changes in wind and cloudiness, changing energy production from wind turbines and solar panels. The basic idea in NWP nowcasting (even more in general nowcasting), is to utilise very recent observations to predict near future events. Cycling a forecasting system 4 times a day, every 6 hour, to predict the exact strength and location of a one or two hour convective precipitation event is beyond the capacity of the current observing systems and NWP models. Possibly beyond physics as well (chaos/un-predictability). CASE 1 – 2/7-2011 Copenhagen 10-minute output 15 UTC simulation CASE 2 – 14/8-2010 - Copenhagen Subjective verification Objective verification of precipitation The ”double penalty problem” of high resolution models when using standard point verification At half the resolution Point comparisons of precipitation tend to punish high resolution models relative to coarser resolution models, even if to a forecaster they appear superior. FSS (fractions skill score) CASE 1 – 2/7-2011 Uniform Fractions skill score CASE 1 – 2/7-2011 CASE 2 – 14/8-2010 Fractions skill score Ensemble forecasting The NWP models are far from perfect. Both because of lack of computer power and lack of physical knowledge about important processes. The initial conditions are heavily under-determined by the observations. Some of the most severe weather events in Europe are related convective precipitation, which can have very short lifetime, hour to hours, and very low predictability. The atmosphere is a chaotic system. Small variations in initial conditions can lead to large variations in the forecast. Ensemble forecasting By making variations of the initial conditions and the unknowns of the NWP model, in a systematic and realistic way, we can assess the quality and robustness of the forecasts, enabling estimation of the uncertainty of the forecasts, as well as identify situations where several outcomes (forecasts) are possible, given our lack of perfect models and lack of a perfect observing system. Running such a suite of forecasts in called “Ensemble forecasting”. Originally ensembles where global, with a focus on large scales and several days ahead. Now many regional ensembles exist, with a focus on the near future and smaller scale phenomena, such as severe, convective precipitation. Example from the ECMWF ensemble system with 50 members (different forecasts). Ensamble prediction for a single location. Next slides show results from a DMI ensemble with a resolution of 5 km and 25 members (different forecasts). Ensemble prediction, rainfall 14 Aug 2010 Ensemble mean and forecast “probabilities” Access to NWP models • Some NWP models, such as WRF and MM5 are open software, that you can download and run on your pc. They are used extensively for research at universities, resulting in a wealth of different software packages to choose between for simulations of various physical processes, assimilation of different observations, etc. • In addition it is possible to download freely GFS data, which can be used as initial data and boundary data for your own NWP run. • In contrast the majority of the NWP models and associated data assimilations systems used for operational weather forecasting at the national met offices are not open software. They are developed by consortias of met offices, some by single met offices. They benefit from being developed in a ”balanced” way, each component constructed to work well with the other components.