Regional climate model formulation

Regional climate model formulation
PRECIS Workshop, Reading University, 23rd – 27th April 2012 © Crown copyright Met Office

Goal of session To provide an overview of the scientific formulation of PRECIS © Crown copyright Met Office

General Description Global/Regional climate models are models of the climate system, including the atmosphere, oceans, land-surface and more. The advective (relating to motion) and thermodynamical (relating to heat) evolution of atmospheric pressure, winds, temperature and moisture (prognostic variables) are simulated, while including the effects of many other physical processes. Other useful meteorological quantities (diagnostic variables) are derived consistently within the model from the prognostic variables, such as precipitation, evaporation, soil moisture, cloud cover and many more. © Crown copyright Met Office © Crown copyright Met Office 3

Main components of global climate models
Atmospheric dynamics Model grid Physical parameterizations Initial and boundary conditions of the model © Crown copyright Met Office © Crown copyright Met Office 4

Atmospheric dynamics The evolution of pressure, winds, temperature and moisture are governed by the laws of energy and conservation. Conservation of momentum Conservation of mass Conservation of energy The atmospheric dynamics is the part of the RCM which, in essence, uses three fundamental conservation principles to simulate atmospheric pressure, wind, temperature and moisture, and these are the principles of … … and the actual mathematical equations which are solved within the dynamical part of the model are ultimately derived from these assumptions about the atmosphere. © Crown copyright Met Office © Crown copyright Met Office 5

Horizontal equation of motion (the conservation of momentum)
Newton’s 2nd law: Force = Mass  Acceleration The change in velocity of an air parcel is dependent on the Coriolis force the pressure gradient force gravity friction Looking in more detail at these principles, first we have the conservation of momentum, which is expressed according to Newton’s 2nd law and which gives us the equation of horizontal motion - the equation that we use to simulate the movement, or advection, of parcels of air around the atmosphere, or in other words, the winds. Newton’s 2nd law states that the force acting on a body is equal to its mass multiplied by its acceleration, and in our context we express this as: The acceleration of an air parcel (of unit mass and following the relative motion in the rotating frame) equals the sum of the Coriolis force (the apparent force which results from movement within a rotating system), the pressure gradient force (the force due to changes in the horizontal pressure field), effective gravity and friction. It is this form of the momentum equation that is basic to most work in dynamic meteorology. ______________________________________________________________ Newton's 2nd Law of Motion states that the acceleration of a particle is equal to the vector sum of forces acting upon that particle. It is a statement of the Conservation of Momentum principle. The main forces in the atmosphere are the force that acts on air due to differences in pressure and the Coriolis Force. The Coriolis Force (or acceleration) is an apparent acceleration that air possesses by virtue of the earth's rotation. If an air parcel is moving between two points then its path, relative to the surface of the earth, will not be straight but will be curved. The curve will be towards the right in the northern hemisphere and to the left in the southern hemisphere. It is sometimes convenient to represent the horizontal equation of motion in its two components. © Crown copyright Met Office © Crown copyright Met Office 6

The hydrostatic assumption (taking vertical motions out of the model)
At synoptic scales, vertical accelerations due to the conservation of momentum are small and may be ignored. Newton’s equation in the vertical then simplifies to Relates vertical pressure variations with gravity and atmospheric density I.e. there are only two explicit forces acting in the vertical (pressure gradient force and gravity) and these act to cancel each other out We have considerably simplified Newton’s equation by only considering horizontal motions, that is those parallel to the earth’s surface. Vertical motions were removed, for the time being at least, by applying the hydrostatic equation which relates vertical variations in pressure with height above the earth’s surface. This is assuming that there are only two forces acting in the vertical and that these forces act to cancel each other out. Therefore vertical velocities and accelerations are not explicitly modelled in this RCM. We can physically justify this assumption by noting that at the synoptic scales of the model, the magnitudes of vertical motions are small compared to horizontal velocities and accelerations. _____________________________________________________________ The hydrostatic equation is an expression relating the variation in pressure with height. In the vertical the two main forces are gravity and the pressure gradient. In fact, the gravitational force is almost exactly balanced by the pressure gradient force i.e. the air's buoyancy, a condition known as hydrostatic equilibrium. The vertical component of the Coriolis Force, although comparable in magnitude with the horizontal components, is negligible when compared against the gravitational and pressure gradient forces. For this reason it is often ignored but our model does include it although in practice it is only significant in regions of strong vertical motion. © Crown copyright Met Office

Hydrostatic equilibrium
TOA Pressure decreases with Mass of air parcel: height: downwards force due to upwards ‘pressure gravity gradient force’ acting through the parcel This diagram describes the hydrostatic assumption. For a parcel of air, anywhere between the surface of the earth and the top of the atmosphere, the presumed balancing of the two opposing forces gives the air parcel neutral buoyancy, and so no explicit vertical movement. ______________________________________________________________ The hydrostatic equation is an expression relating the variation in pressure with height. In the vertical the two main forces are gravity and the pressure gradient. In fact, the gravitational force is almost exactly balanced by the pressure gradient force i.e. the air's buoyancy, a condition known as hydrostatic equilibrium. The vertical component of the Coriolis Force, although comparable in magnitude with the horizontal components, is negligible when compared against the gravitational and pressure gradient forces. For this reason it is often ignored but our model does include it although in practice it is only significant in regions of strong vertical motion. Earth © Crown copyright Met Office

Vertical equation of motion (the conservation of mass)
The continuity equation: Relates changes in density with divergence in the wind velocity field. Vertical motions are inferred from areas of convergence and divergence in the horizontal wind field (and assuming incompressibility of the atmosphere). Areas of convergence and divergence in the horizontal diagnose a vertical transfer of mass between vertical layers. The model is constructed to conserve mass in the sense that matter may not be created or destroyed, or in other words, the atmosphere is considered a continuum of gas and therefore voids in the atmosphere are not allowed. A consequence of this principle allows us to infer the vertical motions in the atmosphere which were taken out of the conservation of momentum equation by the hydrostatic assumption. We do this by looking at where the horizontal wind field is diverging or converging. This works because in areas where the horizontal wind field is diverging (for example), we can infer the vertical movement of air that is required to fill the void which would otherwise occur in the horizontal divergent field, and it is by this implicit mechanism that the model can simulate vertical motions. © Crown copyright Met Office © Crown copyright Met Office 9

Atmospheric heat and moisture (the conservation of energy)
First law of thermodynamics: heat added = change in internal energy + work done Equation of state for a gas : Temperature and water vapour are also advected Temperature/moisture at a point in the atmosphere can change either due to cooler or warmer/drier or moister air being blown to that point (advection), or from local effects such as evaporation or condensation arising from the equation of state and the first law of thermodynamics Modelling the evolution of heat and moisture at a point in the atmosphere appeals to the final conservation principle, that of the conservation of energy, which is applied to a moving atmospheric (fluid) element according to the first law of thermodynamics and the equation of state for a gas. With the first law of thermodynamics we adhere to the principle that ‘The amount of heat added to a system, in this case a parcel of air, is exactly balanced by the work done in increasing its volume and the change in internal energy’ and the equation of state relates: p=vapour pressure, v=specific volume, R=gas constant, T=temperature And what we end up with, remembering that temperature and moisture may be advected around with the large scale air flow, is that the temperature/moisture at a point in the atmosphere can change either due to cooler or warmer/drier or moister air being blown to that point, or from local effects such as evaporation or condensation arising from the equation of state for a gas and the first law of thermodynamics. ______________________________________________________________ The 1st Law of Thermodynamics may be stated as the amount of heat added to a system is exactly balanced by the work done in increasing its volume and the change in internal energy. It is an expression of the principle of the conservation of energy which states that the change in energy within a system is equal to the net transfer of energy across the boundaries of the system. The equation of state relates the three primary thermodynamic variables, pressure, density and temperature for a perfect gas. However, a perfect gas does not exist but real gases can be assumed to still obey the equation. The atmosphere, despite being a mixture of gases, is also assumed to obey the equation. Temperature at a point in the atmosphere can change either due to cooler or warmer air being blown to that point, known as advection, or from local effects such as evaporation or condensation. © Crown copyright Met Office © Crown copyright Met Office 10

Discretizing the model equations
All model equations are solved numerically on a discrete 3-dimensional grid spanning the area of the model domain and the depth of the atmosphere and ocean The model simulates values at discrete, evenly spaced points in time The period between each point in time is called the model’s timestep Spatially, data are average over a grid box Temporally, data can be assumed to be instantaneous o We now have a set of equations which describe the evolution in space and time of the prognostic variables (pressure, wind, temperature and moisture), but these equations are not solvable analytically. So we calculate their solution numerically at points on a discrete 3-dimensional grid which spans the horizontal domain of the model and the whole depth of the atmosphere. The calculations are also only carried out at discrete, evenly spaced points in time, and we call the time gap between each of these the model’s timestep. Furthermore, the formulation is such that the data produced \by the model equations at a point in space is in fact an average quantity over the whole of the grid box that it lies in the centre of, but the same data at a point in time is instantaneous data, or in other words it is not an average over a whole timestep but is only valid at that one instant. (E.B. version: The assumption that data are instantaneous is probably based on the numerical propagation scheme. By taking the point of view of the basic equations, however, it is quite clear that the same reasoning which applies to parametrization, averaging processes in space AND time, should be applied to the dynamics as well) Overall, this process of approximating the solution at individual points in both space and time one of discretization. time © Crown copyright Met Office © Crown copyright Met Office 11

The three dimensional model grid
Vertical exchange between layers of momentum, heat and moisture Horizontal exchange between columns of momentum, heat and moisture 15° W 60° N 3.75° 2.5° Vertical exchange between layers of momentum, heat and salts by diffusion, convection and upwelling 11.25° E Vertical exchange between layers by diffusion and advection 47.5° N Orography, vegetation and surface characteristics included at each grid box surface © Crown copyright Met Office © Crown copyright Met Office 12

Length of timestep The numerical stability criterion for this model insists that we can not allow a parcel of air to travel more than one grid length in distance in one timestep Knowledge of the grid length and maximum wind speeds will give the maximum possible timestep time = distance/speed Assuming maximum wind speed, u = 166 ms-1 ~150km resolution  15 minute timestep ~50km resolution  5 minute timestep ~25km resolution  2.5 minute timestep It turns out that the length of the timestep in the model needs to be chosen carefully, as whilst we are technically free to choose any horizontal grid spacing, or resolution, that we want, once we have done that we are limited in our choice of the length of the model’s timestep. This is because the model’s numerical integration scheme has been designed to adhere to the rule that we can only allow a parcel of air to travel at most one grid box length in one timestep. But this is easy to deal with, as the basic time = distance/speed equation will tell us the maximum timestep allowed, given that we know the maximum possible wind speed and the size of a grid box. What we come up with, assuming that wind speeds never exceed 166 m/s anywhere in the atmosphere, are the following timesteps for the horizontal resolutions of the driving AGCM, the 50km and the 25km regional models, and as expected the timestep gets shorter as the size of the grid boxes decreases. © Crown copyright Met Office

Atmosphere and ocean dynamics Model grid Physical parameterizations Initial and boundary conditions of the model © Crown copyright Met Office © Crown copyright Met Office 14

The model grid Hybrid vertical coordinate
Combination of terrain following and atmospherics pressure 19 vertical levels (lowest at 50m, highest at 5Pa) Regular lat-lon grid in the horizontal ‘Arakawa B’ grid layout P = pressure, temperature and moisture related variables W = wind related variables W P Now back to the model grid, which is very important as this is the grid on which all of your model results will be on. The vertical component of this grid uses a so called hybrid coordinate system. It is hybrid in the sense that each vertical level is specified as a linear combination of a terrain following height-above-the-surface coordinate and an atmospheric pressure coordinate. The number of levels is fixed at 19: the lowest four are purely terrain following, the uppermost three near the top of the atmosphere are purely pressure levels and levels 5 to 16 are a fixed linear combination of the two types of coordinate. Within each vertical level is a horizontal grid which uses a latitude/longitude spherical polar coordinate system with regular grid spacings in both latitudinal and longitudinal directions. And furthermore, within this horizontal grid the wind variables are simulated on a grid that is offset by half a grid box in each direction from all of the other variables. This particular layout of two staggered horizontal grids is known as an ‘Arakawa B grid’ and is used for its numerical stability properties. © Crown copyright Met Office

The rotated pole The coordinate pole of the RCM grid is usually rotated The RCM’s north pole is not in the usual position This ensures numerical stability without the need for non-physical filtering Avoids high latitudes where filtering is necessary RCM grid boxes are quasi-regular in area All grid boxes are near the equator The horizontal grid used in PRECIS has yet more complexity, as its spherical polar coordinate system is rotated around the earth so that equator of the coordinate system approximately bisects the region of interest, and therefore the RCM’s coordinate north pole is unlikely to be in its usual position in the arctic. The reason we do this rotating is due to the fact that for a regular latitude-longitude grid in spherical polar coordinates, the area covered by a grid box decreases as you move further away from the equator towards the poles as the lines of constant longitude converge. We find that above about 60 degrees of latitude, the grid boxes have become small enough to affect the numerical stability of the model, as it becomes possible for a parcel of air to travel more than one grid box length in one timestep. In the global version of the atmospheric model, where we can not avoid high latitudes, this difficulty is overcome by a non-physical filtering out of the resulting instabilities at the higher latitudes. However since RCMs are of limited area, typically spanning at most 50 or 60 degrees from top to bottom, by shifting the equator to lie inside of our domain we can ensure that there are no high latitudes above 60 degrees in the anywhere in the model’s domain and so the unrealistic filtering is not necessary. It also gives the practical advantage that all of the grid boxes in the domain will cover approximately the same area of the earth’s surface, which is useful when analysing the results, as no area weighting of the data for each grid box needs to be done. © Crown copyright Met Office

Rotated pole example Full RCM domain on its own rotated lat-lon grid
This diagram exemplifies the relationship between the RCM’s rotated grid and the familiar unrotated, regular latitude-longitude grid. In both pictures, the solid lines denote constant latitudes and longitudes in the rotated coordinate system of the RCM and dashed lines denote constant latitudes and longitudes in the familiar unrotated coordinate system The left hand picture shows the area spanned by a RCM on its own grid and the right hand picture shows the same area represented on the unrotated grid. So we see that the RCM domain is a nice, regular shape when viewed on its own coordinate system, but has an irregular, curved outline when this area is projected onto the usual unrotated coordinate system, and this will need to be considered when plotting the RCM results, or comparing the RCM results with GCM or observational data, which almost invariably will be on the unrotated grid. Full RCM domain on its own rotated lat-lon grid Full RCM domain projected onto the regular lat-lon grid © Crown copyright Met Office

Physical processes This section is about including in the model the effects of many other physical processes in the atmosphere and land surface of the climate system which haven’t been accounted for by the grid scale simulation of the prognostic variables by the atmospheric dynamics. © Crown copyright Met Office

Parameterization of physical processes
Important processes occur in the atmosphere on scales smaller than those which are resolved by the grid of the dynamical part of the model. The effects of these unresolved (sub-grid scale) processes are deduced from the large scale state variables predicted by the model (wind, pressure, temperature, moisture). This procedure is called parameterization. The reason that some other physical process are treated differently to the dynamical part of the model is that these important processes occur on spatial scales much smaller than that which is resolved by the discrete 3-dimensional grid on which the dynamical equations are calculated. What we can do, however, is to deduce the grid scale effects of these unresolved sub-grid scale processes from the large scale state of the atmosphere as given by the prognostic variables arising from the dynamical equations, and we call this technique parameterization. © Crown copyright Met Office © Crown copyright Met Office 20

Physical parameterizations
Some examples: Clouds and precipitation Radiation Atmospheric aerosols Boundary layer Land surface Gravity wave drag I have split the physical parameterizations within PRECIS into six main groups, and whilst there is no time here to do each topic justice, I’ll hopefully give an idea of the varying levels of complexity involved in the modelling of these sub-grid scale processes. The strategy or method in which a sub-grid scale process is parameterized by the model is referred to as a scheme. Many different schemes for dealing with various physical processes have been developed by climate scientists. Each climate model (including PRECIS) will use a different set of schemes as part of its unique formulation. © Crown copyright Met Office © Crown copyright Met Office 21

Clouds and precipitation
‘Large scale’ and convective processes are treated separately In general: Cloud droplets may be liquid or frozen Precipitation is partitioned into snow (solid) and rain Solid/liquid/large scale/convective/total precipitation data are output by the model as separate diagnostics See STASH codes 4203, 4204, 5205, 5206, 5216 in Appendix C Cloud formation and precipitation are partitioned into two types within the model, the so called large scale and convective processes. I’ll elaborate on each on the next couple of slides, but there are some features common to both parameterizations. We have that cloud water droplets may be liquid or frozen in the model, as is the case for falling precipitation. Also, both solid and liquid precipitation are diagnosable, or outputtable, from both the large scale and convective precipitation schemes. © Crown copyright Met Office

Large scale clouds and precipitation
Results from the large scale movement of air masses affecting grid box mean moisture levels Due to dynamical ascent (and radiative cooling and turbulent mixing) Cloud water and cloud ice are simulated Conversion of cloud water to precipitation depends on the amount of cloud water present precipitation falling into the grid box from above (seeder-feeder enhancement) Precipitation can evaporate and melt Large scale clouds and precipitation are so called because they arise from the large scale movement of air masses affecting grid box mean moisture levels. Dynamical assent is the main cause for the formation of large scale cloud, but radiative cooling and turbulent mixing are also causes, the latter especially in the boundary layer. The large scale cloud model calculates the fraction of a grid box which is cloudy and also the mixing ratios for cloud water and cloud ice. When cloud is present in a grid box, the autoconversion of cloud water to precipitation depends on the amount of cloud water present and also on any precipitation falling into the grid box from above (seeder-feeder enhancement). Evaporation and melting of precipitation are also considered. _____________________________________________________ The model holds explicit values of fractional cloud cover, together with separate values for cloud water and cloud ice mixing ratios (i.e. kg of cloud water/ice per kg of moist air within a cloud). Cloud water is converted to precipitation by a process known as autoconversion, the rate of which increases with increasing cloud water mixing ratios. The autoconversion equation includes a term which increases the rate of conversion if there is precipitation falling into the grid-box from above, thereby simulating the processes of growth by accretion and coalescence. In this way seeder-feeder enhancement of precipitation may be represented. Frozen precipitation is assumed to start falling as soon as it is formed, simulating enhanced growth by deposition (Bergeron-Findeisen). Evaporation and melting of precipitation is allowed to take place to the extent that the temperature and humidity of lower layers allow, with the attendant cooling of the environment by latent heat exchange. At temperatures of -9 °C and below, all cloud content is ice, with a mixture of water and ice between -9 and 0 °C, the proportion of ice decreasing with increasing temperatures. Dynamical ascent is the most important process leading to cloud formation in the model, but cloud may also be formed by radiative cooling and turbulent transport. © Crown copyright Met Office

Convection and convective precipitation
Cloud formation is calculated from the simulated profiles of temperature pressure humidity aerosol particle concentration Entrainment and detrainment Anvils of convective plumes are represented Convective clouds are modelled by an updraught dependent on a vertical temperature instability balanced by a precipitation induced cool downdraught. The resulting cloud fraction in a grid box is also dependent on pressure, humidity and aerosol particle concentration, as is also the case with large scale cloud formation. Mixing with environmental air at the cloud edges, known as entrainment and detrainment, is included, and we also parameterize the effects of the anvils of deep convective clouds which are particularly important in the tropics, where they have a large radiative effect. ______________________________________________________________ A cloud model is used to represent cumulus and cumulonimbus convection, in which an updraught and precipitation-induced downdraught are considered. A test is made for convective instability: if the potential temperature of any level is higher than that of the level above, convection is initiated. Convection will continue as long as the air within the cloud continues to be buoyant. Dilution of the cloud is represented by entrainment of environmental air. Before the cloud detrains completely at the level where the parcel of air ceases to be buoyant, the remaining mass, heat, water- vapour and cloud water/ice are completely mixed into the environment at the cloud top. A single cloud model is used to represent a number of convective plumes within the grid square, and precipitation is diagnosed within that square if: (i) cloud liquid/ice content exceeds a critical amount and (ii) the cloud depth exceeds a critical value. This value is set to 1.5km over the sea and 4km over land. However, if the cloud top temperature is less than -10 °C, the critical depth is reduced to 1km over land or sea. As with large-scale precipitation, the convection scheme allows for evaporation and melting of precipitation. © Crown copyright Met Office

Radiation The uneven distribution of solar heating is the ultimate driving force of the general circulation and the original source of all the atmosphere’s available energy It is fair to say that … … and this is particularly relevant in a climate change context, as global warming essentially arises from a perturbation to the radiative equilibrium of the globe. © Crown copyright Met Office

Radiation The daily, seasonal and annual cycles of incoming heat from the sun (shortwave insolation) are simulated Short-wave and long-wave energy fluxes modelled separately SW fluxes depend on the solar zenith angle, absorptivity (the fraction of the incident radiation absorbed or absorbable), albedo (reflected radiation/incident radiation) and scattering (deflection) ability LW fluxes depend on the amount an emitting medium that is present, temperature and emissivity (radiation emitted/radiation emitted by a black body of the same temperature) Radiative fluxes are modelled in 14 discrete wave bands spanning the SW and LW spectra The radiation scheme includes the daily, seasonal and annual cycles of incoming shortwave radiation from the sun, and then within the atmosphere, the model then treats shortwave and longwave radiative fluxes separately. SW fluxes depend principally on the solar zenith angle and on various radiative properties of clouds and the atmosphere, namely absorptivity (the property of a body that determines the fraction of the incident radiation absorbed or absorbable by the body), albedo (the ratio of reflected to incident radiation) and scattering (deflection) ability. Having absorbed shortwave radiation, many parts of the system re-emit energy as longwave radiation. LW fluxes depend on the amount an emitting medium that is present, such as a cloud or part of the earth’s surface, its temperature and its emissivity (radiation emitted/radiation emitted by a black body of the same temperature) We also know that the effects of various radiatively active atmospheric constituents are all different – constituents such as CO2, ozone, sulphate particles, H20. So to help treat these constituents differently in the model, radiative fluxes are simulated in 10 discrete wave bands of the electromagnetic spectrum spanning the SW and LW ranges (4 SW, 6 LW). __________________________________________________________________________ The atmosphere is driven by solar radiation and thus an accurate representation of radiative processes is essential for weather forecasting models. Radiation in the atmosphere is divided into short-wave and long-wave. Short-wave is due to incoming solar radiation and may be absorbed by clouds, atmospheric gases and the earth's surface or reflected back into space. The amount of short-wave radiation reflected depends upon the reflectivity, or albedo, of the surface. Long-wave radiation is that emitted by clouds etc. The albedo of the Earth's surface is dependent upon the vegetation type and is specified as an ancillary file. Short-wave fluxes depend principally on the solar zenith angle (varying according to latitude, season and time of day), cloud and the albedo of the surface. Long-wave fluxes depend upon the amount and temperature of the emitting medium and its emissivity. The effects of each radiatively active constituent of the atmosphere (water vapour, carbon dioxide and ozone) are quite different and must be calculated separately. For this reason long-wave radiation is considered in six wavebands and short-wave in four. Clouds interact to a significant degree with both long and short-wave radiation. They are treated as homogeneous plane-parallel slabs, and in any grid-square a number of layers are allowed together with one convective tower. Their effects depend upon fractional cover, height, phase and water/ice content. "Dynamical ascent is the most important process leading to cloud formation in the model". Radiative heating and cooling rates are highly dependent upon water, in the form of both vapour and cloud/ice water content. Unfortunately the water substance as a whole is poorly observed in the atmosphere and therefore the least well-forecast of all primary model variables. © Crown copyright Met Office

Atmospheric aerosols The spatial distribution and life cycle of atmospheric sulphate aerosol particles are simulated Other aerosols (e.g. soot, mineral dust) are not included Sulphate aerosol particles (SO4) tend to give a surface cooling: The direct effect (scattering of incoming solar radiation  more solar radiation reflected back to space) The first indirect effect (increased cloud albedo due to smaller cloud droplets  more solar radiation reflected back to space) Natural and anthropogenic emissions are prescribed source terms (scenario specific) Closely linked to the cloud and radiation schemes is the treatment of atmospheric aerosols, and the RCM can simulate the spatial distribution and life cycle of sulphate aerosol particles in the atmosphere. This scheme, whilst optional in the PRECIS model, is particularly important in a climate change context as the presence of such particles tends to give a surface cooling effect, thus offsetting some the GHG induced warming in some areas. There are two mechanisms in the model which can lead to this cooling effect … (A third mechanism by which sulphate aerosol particles can affect the atmosphere, known as the second indirect effect, is not included in the model. This is an effect which arises from the lifetime of clouds being increased by the presence of atmospheric aerosols. (smaller droplets  longer lasting clouds)) Now, in the model, sulphate aerosol particles (SO4) exist in the atmosphere ultimately due to the emission of chemicals from the earth’s surface. These emissions occur from natural sources, such as SO2 from active volcanos and dimethyl sulphide (DMS) released from the surface of the oceans, and also anthropogenic, or human made, sources, such as SO2 released from fossil fuel burning mainly in industrial areas. In both cases time varying source data are part of the model, for both current and future climates. © Crown copyright Met Office

Anthropogenic surface and near-surface SO2 emissions
This picture shows anthropogenic SO2 emissions averaged over the month of January 1960.We can clearly see the localized nature of the emissions, centred around the most industrialized areas, and as the lifetime in the atmosphere of the resultant sulphate aerosol particles is at most a week or two, the surface cooling effect that they have tends to be localized to around the areas of emissions. © Crown copyright Met Office

Boundary layer processes
The atmospheric or planetary boundary layer is the part of the atmosphere which is directly influenced by the surface. A few tens of metres to 1-2 km deep depending on the stability Next we have processes occurring in the atmospheric boundary layer, which may be thought of as the part of the atmosphere which is directly influenced of the earth’s surface. It is very variable in depth, ranging from a few tens of metres thick over the nighttime desert, up to a couple of kilometres in areas of active convection. © Crown copyright Met Office

Boundary layer processes
Turbulent mixing in the lower atmosphere Sub-gridscale turbulence mixes heat, moisture and momentum through the boundary layer The extent of this mixing depends on the large scale stability and nature of the surface Vertical fluxes of momentum ground  atmosphere Fluxes depend on atmospheric stability and roughness length Within the atmospheric boundary layer, heat, moisture and momentum are mixed by subgrid scale turbulence, and this turbulent mixing is dependent on the large scale vertical temperature stability of the atmosphere, and on the nature of the land surface. Also modelled are fluxes of momentum between the atmosphere and the ground, and again this depends on the atmospheric stability and the nature of the earth’s surface - in particular the roughness length, which is a measure of how far the physical nature, or roughness, of the of the surface can influence up into the atmosphere. © Crown copyright Met Office

Surface processes: MOSES
Exchange of heat and moisture between the earth’s surface, vegetation and atmosphere Surface fluxes of heat and moisture Precipitation stored in the vegetation canopy Released to soil or atmosphere Depends on vegetation type Heat and moisture exchanges between the (soil) surface and the atmosphere pass through the canopy Sub-surface fluxes of heat and moisture in the soil 4 layer soil model Root action (evapotranspiration) Water phase changes Permeability depending on soil type Run-off of surface and sub-surface water to the oceans Moses II: tiled representation of sub-grid heterogeneity Changed vegetation types with respect to Moses I q, T As well as fluxes of momentum between the atmosphere and the earth’s surface, we also model exchanges of heat and water between the atmosphere, the earth's surface and the deeper soil with a parameterization known as MOSES1. On the land surface, MOSES1 stores precipitation in the vegetation canopy. This water is released either to the soil via throughfall or back to the atmosphere by evaporation, and the amount of water the canopy in a grid box can hold is dependent on the plant types present in the grid box, of which there are 53 possible types. Also the effects that the vegetation canopy have on the deep soil to atmosphere heat and moisture fluxes are also included. Beneath the surface, fluxes of heat and moisture are simulated with a 4 layer soil hydrology and thermodynamic model. This includes the effect of roots, which remove water from the soil back to the atmosphere by transpiration, ground water phase changes, so ground frosts are simulated and permeability of the soil depending on soil type, such as sandy or clay-like soils (22 types). Finally, ground water can run off, ultimately to the oceans, and this is partitioned into surface and sub-surface components. _______________________________________________________________________ Each land point is assigned characteristics according to the soil type and the vegetation type. These are important in the calculation of the heat, moisture and momentum fluxes at each grid point. If land is covered by snow then the properties, such as albedo, will be drastically altered. The soil temperature is calculated in four separate levels. The temperature of the soil will change according to the radiation balance at the soil surface. Snow cover will act as an insulator to the soil. Each land point has a value of the soil moisture content in four layers of different thicknesses which is altered according to how much evaporation is occurring and the amount of precipitation at that point. The vegetation plays an active role in the hydrology at the surface. When precipitation falls some is intercepted by and held in the canopy of the vegetation. The remainder is known as canopy throughfall and falls to the soil's surface. This water is absorbed by the soil unless the intensity is too great or the soil is already saturated in which case surface runoff, into rivers and lakes, occurs. Soil water is primarily lost though evaporation through plants, in which case the term transpiration should be used. The amount of transpiration that can occur is limited by the soil moisture, as the soil dries it becomes progressively more difficult for plants to extract water. Over the sea the roughness length, a representation of surface drag, is increased with increasing wind speed to represent the interaction with waves. © Crown copyright Met Office

Gravity wave drag Flow over mountains can generate waves in the atmosphere Waves can propagate vertically, reducing stability These waves exert a drag on the flow Orientation of orography is taken into account Wind direction The final parameterization is that of gravity wave drag, which describes how flow over mountains generates sub-grid scale atmospheric waves. These waves form on the lee side of mountains and propagate vertically, reducing stability in the atmosphere and thereby exerting a drag on the prevailing horizontal flow. It is important because it has been found that without the scheme, and the drag that it generates, the jet streams in the model tend to be too strong and this feeds back to overly deep surface depressions and a poorer surface climatology. A further point is that the subgrid scale geographical orientation of mountain ranges is taken into account by storing information of the 3-dimensional standard deviation of the surface topography. _________________________________________________________________________ The Unified Model includes a scheme to parameterize gravity wave drag, whereby flow over mountains in stable conditions excites waves. The stress exerted depends on the low level wind speed and static stability, as well as the variance and anisotropy of the sub-grid orography. For high Froude number flows, the response is modelled on the generation and propagation of linear hydrostatic waves. Additionally, trapped lee waves are represented when the vertical profile of the Scorer Parameter is found to be favourable. When the Froude number is small (close to unity), the hydraulic jump type of flow response, also known as the high drag state, is triggered instead. The GWD effect is largest over mountains in winter, where it reduces the strength of jet streams and causes surface depressions to be less deep and quicker to fill than would otherwise be the case. The orographic form drag scheme parameterizes the effects on the boundary layer of sub-gridscale topography on scales of 10km or less. The form drag is calculated in terms of a constant drag coefficient and depends linearly on the silhouette area of orography, which is measure of the slopes within a grid box. It uses an effective roughness length which is a combination of the effects of the topography and vegetation. The standard formulae given by Monin-Obukhov theory are then used to calculate the surface fluxes. © Crown copyright Met Office

Initial conditions All climate models require information about the initial state of the atmosphere at the beginning of the climate model experiment. These are the initial conditions of the model experiment. At the beginning of an experiment, the RCM needs values for all of the prognostic variables throughout the atmosphere and deep soil. Derived from the same source as the driving GCM or reanalysis experiment © Crown copyright Met Office © Crown copyright Met Office 34

Boundary conditions The three dimensional grid of a GCM has no lateral (North- South, East-West) boundaries. The upper boundary is the end of the atmosphere where it contacts outer space. The lower boundary is either the surface of the land or the bottom of the ocean. As such the GCM (and RCM) require information about the topography of the Earth’s surface, called surface boundary conditions. As RCMs model a limited area, they have an additional requirement of having “input” data provided for them at their outside edges, i.e. their lateral boundaries. © Crown copyright Met Office © Crown copyright Met Office 35

Lateral Boundary Conditions
LBCs = Meteorological boundary conditions at the lateral (side) boundaries of the RCM domain They constrain the prognostic variables of the RCM throughout the simulation ‘Driving data’ comes from a GCM or analyses Lateral Boundary condition variables: Wind Temperature Water vapour Surface pressure Sulphur variables (for Hadley Centre GCMs) Given that RCMs are limited area models they need to be provided with values of the prognostic variables at their edges, and these time-dependent large-scale data, which we call the lateral boundary conditions (LBCs), constrain the RCM at its edges throughout the simulation. The data for the LBCs come either from existing GCM integrations or from analyses of observations, and are applied over a buffer zone at the edge of the domain of 4 grid points in width. Therefore the RCM is only completely freely evolving outside of this buffer zone in its interior, and so the results over this rim must be discarded from any analysis that is carried out on the data. © Crown copyright Met Office

Other boundary conditions
Information required by the model for the duration of a simulation Constant data applied at the surface Land-sea mask Orographic fields (e.g. surface heights above sea level, StDev of altitude) Vegetation and soil characteristics (e.g. surface albedo, height of canopy) Time varying data applied at the surface SST and SICE fractions Anthropogenic SO2 emissions Dimethyl sulphide (DMS) emissions Time varying data applied throughout the atmosphere Atmospheric ozone (O3) Greenhouse gases (CO2, CH4, N2O, CFCs) concentrations from the same emission scenario used by drivng GCM or historical if reanalyses are used Constant data applied throughout the atmosphere Natural SO2 emissions volcanos Annual cycle data applied throughout the atmosphere Chemical oxidants (OH, HO2, H2O2, O3) These are referred to In PRECIS as “ancillaries” and are found in the $ANCIL_MASTER directory Finally we have all of the rest of the boundary conditions, which are provide information that is required throughout the duration of a simulation, but which are not the lateral boundary conditions. Spatially, these are applied either at the surface only or throughout the depth atmosphere, and temporally they are applied either as data which is constant in time, as non-repeating time-varying data or as periodic data which repeats an annual cycle. © Crown copyright Met Office

Summary Models utilise a finite three-dimensional resolution and timestep Models solve (integrate) the governing differential equations of mass, momentum and energy Sub-grid scale processes are parameterized Prognostic variables take information from timestep to timestep Other quantities diagnosed – diagnostic variables Initial conditions and boundary conditions are necessary components of the model. Climate models attempt to represent the evolution of the atmosphere, and other sub- components of the Earth system, using a (necessarily limited) amount of information. There are two types of model in use: grid point models, where the values of the model variables are held on the vertices of a grid whose resolution can be specified, and spectral models, where fields are represented by a superposition of waves of differing frequency and the limitation is on the frequency of the waves represented. The models evolve in time through numerical solution of the differential equations governing the system of interest. Model runs are sometimes referred to as “integrations”, because the aim is integrate the equations, for the prevailing conditions; this has to be done in some approximate way for a finite updating interval or “timestep”. In grid point models, values at adjacent grid points are used to calculate the required spatial derivatives. The timestep should in general be chosen so that information propagating across the grid cannot travel across more than one grid box in each timestep – effectively, higher resolutions require smaller timesteps. Model variables that are solved for directly are known as “prognostic” variables. For a model of the atmosphere they are typically wind, surface pressure and some representation of temperature and moisture. (There are neat ways of representing temperature and moisture which when used together allow, for example, partition of moisture into water vapour and liquid water phases). Prognostic variables are treated in a physically consistent manner from timestep to timestep. Other variables are “diagnosed”, that is, derived directly or indirectly from the prognostic variables at each model timestep. PRECIS uses a grid-point model. Models covering the whole of the globe using a latitude/longitude grid can have problems at high latitudes (near the poles), where the model grid-points become close together, so filtering of the fields is performed at high latitudes. (This is not a problem in spectral models; these however have a large computational overhead in conversion between grid-point space and spectral space.) The atmosphere of course is dependent on other systems for its “boundary conditions”. These systems may be represented by another model, running simultaneously, with passage of information between the two – this is known as coupling. These other models have their own prognostic variables. Alternatively, the variables required at the boundaries may be supplied by prescribed fields – constant or with a seasonal cycle. © Crown copyright Met Office © Crown copyright Met Office 38

Regional climate model formulation

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Regional climate model formulation

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