It should be noted from Chapter 5 that although the term dynamical downscaling is used to describe the application of RCMs or LAMs to produce rainfall at local scales, based on GCM output, what is done is in fact a full physical simulation of the atmospheric system within the model domain. The GCM output fields are used as lateral boundary conditions and are not limited to precipitation. For dynamical downscaling it is typically necessary to specify pressure, lateral velocity, temperature, moisture content and elevation (geopotential height) as lateral boundary conditions. Clouds and rainfall are generated within the model using the governing equations. While it is possible to specify hydrometeorological variables like cloud density at the lateral boundaries, these are optional and often unnecessary to get good rainfall simulation within the model domain. In this sense, dynamical downscaling is markedly different from statistical downscaling techniques in that it “generates” rainfall based on atmospheric physics (Figure 7.1). Note that both techniques should not be applied separately as the figure suggests, but can be combined, which is most often done.
A primary advantage of dynamic downscaling is the ability to produce a complete set of meteorological variables besides rainfall (e.g. cloud densities in a three-dimensional space, surface temperature on a two-dimensional surface). Since the process of generating rainfall in dynamical downscaling is based on
the atmospheric physics and calculated by solving the governing equations, it is guaranteed that the output quantities are physically consistent with each other. For example, when heavy rainfall happens in a location the cloud formation is always consistent with such a storm activity, so that the expected reduction of shortwave radiation on the earth surface (due to cloud cover) is automatically ensured. While some elementary relationships between various meteorological variables can be embedded in statistical downscaling, it is impossible to achieve complete consistency among all variables.
The dynamically downscaled rainfall is also consistent with local geographical features, for example, topographic variations (Pathirana et al. 2005) and landuse (Shepherd, 2010). This is an important advantage when generating rainfall products for local applications such as urban storm drainage modelling.
On the other hand, dynamically downscaled rainfall does not necessarily show consistency with the large-scale rainfall generated by the GCM that provided the boundary conditions. Suppose a GCM with 100 km×100 km horizontal resolution was used to provide boundary conditions to a RCM with 1 km×1 km resolution. Aggregation of rainfall in the 10000 grid points of the RCM corresponding to a grid point in the GCM would not result in rainfall volumes equivalent to those predicted by the GCM grid. However, it is possible to use GCM rainfall to calibrate and validate the performance of the RCM.
Perhaps the most severe constraint in using dynamical downscaling is the computational expense.
Atmospheric models have three-dimensional grid systems. Therefore, the increase of resolution by a factor of 10 (say 10 km to 1 km) will increase the number of computational cells roughly by a factor of between 100 and 1000 (It is not always necessary to increase the number of vertical levels proportional to the increase of horizontal grids). Due to the nature of numerical implementation of typical RCMs, the computation time-step needs also to be reduced by the same factor to prevent numerical instabilities (say from 10 s to 1 s). Therefore the total computational effort will increase by a factor of 1000 to 10000 when the grid resolution is increased by a factor of 10. This poses considerable challenges in applying dynamical downscaling with the objective of producing a high resolution rainfall product to be used at urban scales.
However, the last two decades have seen an explosive growth of computational power. Today, RCM simulations are routinely performed on consumer grade personal computers. Of course, as explained in Section 5.2, next to the increase in grid resolution and related numerical issues, physical parameterisations have to be changed as well. Below grid sizes of about 3 km, cumulus and convective parameterization are no longer needed and the processes can be modelled explicitly by the model physics, although some problems with non-stationary behaviour remain. Another problem is that the high resolution model is Figure 7.1 The two paths from GCM to local scale rainfall. Statistical downscaling primarily uses“large-scale” GCM rainfall projections and interpolates these values. Dynamical downscaling uses primary atmospheric variables predicted by GCMs and runs local-area models to physically simulate the atmosphere. The latter provides the output of all the atmospheric variables at the finer scale (P: pressure;T: temperature; (u,v):
horizontal velocity components;θ: moisture content; BC: boundary conditions).
nested in a coarser driving model that involves different parameterization schemes. The RCMs moreover most currently do not include coupling between ocean and atmosphere (Wang et al.2004). Questions also remain about the extent to which RCM biases in rainfall results are inherited from the driving model.
Climate model users most often apply dynamical downscaling up to the level of the highest resolution RCMs available, after which point further statistical downscaling may be required. This is not always a good approach. The previous chapter discussed how high resolution RCMs may fail to adequately describe the local surface processes over heterogeneous regions. In these cases, one could argue that a better approach would be to make use of the lower resolution climate model results and an extra statistical downscaling step (Dibikeet al.2008). Other authors have shown that in some cases the RCM based dynamical downscaling method slightly outperforms statistical methods in projecting daily rainfall extremes, as was the case in the test made by Vracet al. (2007a). The question is whether, due to the parametric representation of the precipitation processes, simulation results from current RCMs should be extracted at very fine scales. Below which scale the climate models should not be used is, however, a debatable question (about 30 min or 1 hour and about 3 km?). It depends on the spatial scale at which cloud formation and convection processes can be simulated explicitly without the need to use physical parameterisations (see Section 5.2).
Less debatable is that below the scales of available RCM runs, further downscaling needs to be done using statistical methods. The basic principle of statistical downscaling is to use empirically-based relationships to convert the coarse-scale climate model outputs to rainfall data at the finer urban drainage scales. In this approach, the coarse-scale climate model based information is used as basis for the prediction. These are calledpredictors, while the fine-scale rainfall results are termedpredictands.
Figure 7.2 shows that, while for other hydrological applications such as water supply, irrigation, river hydrology and rainwater harvesting, no temporal downscaling is required, urban hydrology should involve both spatial and temporal downscaling. The rainfall generating processes indeed occur over temporal scales ranging from multi-decadal to sub-minute resolutions with corresponding changes in spatial scales. For urban drainage one has to go down to the minute resolution.
Figure 7.2 Statistical downscaling of RCM outputs down to the scale required for urban hydrological impact studies requires both temporal dowscaling (a–b) and spatial downscaling (b–c) (adapted from Arnbjerg-Nielsen, 2008).
The statistical model can only be based on historical data, thus assuming that the transfer from the predictors to the predictands will not significantly change under changing climatic conditions.
Statistical downscaling methods have the advantage of being computationally inexpensive, and are potentially able to produce finer spatial scales than dynamical methods that use RCMs. Different types of methods exist, each with very specific underlying assumptions. These are presented in the following sections.
Section 7.2 starts with thedelta changemethod, being a fundamental statistical downscaling principle.
Other statistical downscaling methods can broadly be classified into the following three types (Hewitson &
Crane, 1996; Wilbyet al.1998; Nguyenet al.2006; Fowleret al.2007; Vrac & Naveau, 2007):
• Empirical transfer function based methods (Section 7.3);
• Re-sampling methods or weather typing (Section 7.4);
• Conditional probability-based or stochastic modelling methods (Section 7.5).