Downscaling

Good Practice Guidance Paper on Assessing and Combining Multi Model Climate Projections

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A Review of Downscaling Methods for Climate Change Projections

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Downscaling background

Climate change has been exerting important implications for natural environments and human society: from energy supply and infrastructure, to agriculture and ecosystems, at both global and regional scales. The demand for assessments of climate change impacts has grown significantly since the release of the IPCC Third Assessment Report (TAR), particularly for regions which are vulnerable to changes in climate, including the associated changes in frequency and intensity of extreme conditions. Reliable information regarding the rate at which climate changes are occurring and the magnitude of future changes is essential for the development of robust, multi-decadal planning and management strategies. At present, general circulation models (GCMs) are widely recognized as the most appropriate tools for providing the transient global climate simulations and exploring future climate change scenarios.

GCMs are physically based on the principle of fluid dynamics and describe the entire globe using 3-dimensional grids, on which the prognostic equations of the atmosphere are solved to obtain a trajectory of the global climate compatible with the external forcings under given initial conditions. To reduce the enormous calculating requirements, they usually have to use coarse spatial horizontal resolution (in the order of a few hundreds of kilometers) and a set of numerical and parameterization schemes to simplify sub-grid-scale processes and characteristics such as clouds and land use and land cover types (LULC). Although these relative coarse resolutions are generally sufficient to reproduce the main large-scale features of the current climate, they present one of the primary challenges for regional/local climate change impact assessments that typically require high resolution climate change information (in some cases, down to a few kilometers, or even finer)(Robinson and Finkelstein, 1991). Regional climate change impact assessments evaluate the potential impacts of climate change on a specific region to provide key input for the development of adaptation strategies to reduce the vulnerability of human and natural systems to the coming changes.

There is a mismatching in spatial scale between GCM outputs and regional assessments (Robinson and Finkelstein, 1991; Fuhrer et al., 2006; IPCC, 2007a). Thus, it has been an active research field on how to translate projected changes in climate at the semi-continental scale into local conditions relevant to regional impacts assessment. Generally, downscaling techniques are employed to complete such a task (i.e., to derive finer resolution regional-scale or site climate change scenarios from coarser resolution GCM output). They have been widely applied in e.g., hydrological and ecological impact studies.

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Downscaling Methods

In the last couple of decades, a large number of downscaling techniques have been proposed, which can be divided into two main categories: dynamical downscaling (DDSM) and statistical downscaling (SDSM). DDSM nests a regional climate model (RCM) into the GCM to represent the atmospheric physics with a higher horizontal grid box resolution within a limited area of interest. SDSM establishes statistical links between large(r)-scale weather and observed local-scale weather.

There are many comprehensive reviews of downscaling methods and their applications, such as Hewitson and Crane (1996), Wilby and Wigley (1997), Hanssen-Bauer et al., (2005), Christensen et al. (2007) and Fowler et al. (2007). A recent review can be found in Maraun et al. (2010). The following gives a brief summary of SDSM.

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Statistical downscaling

Traditionally, statistical downscaling (SDSM) has been seen as an alternative to dynamical downscaling (DDSM). SDSM essentially consists of employing statistical techniques to establish strong empirical relationships between the GCM simulated large-scale circulation variables (predictors) and the required regional or local scale climate variables (predictands) (Bronstert et al., 2002; Fowler et al., 2007). In other words, it refers to methods in which sub-grid scale changes in climate are calculated as a function of larger-scale climate. The relationship is then exploited to obtain information on the local variable out of the large -scale predictors. The central framework of SDSM can be expressed as:

where p is the local climate variable (predictand), and X is the large-scale state (single or multiple predictors), and F is the function that relates the two and is typically established through a trial-and-error method based on site observations or gridded reanalysis data, and ε is the uncertainty (error) term (van Storch et al. 2000; Fowler et al. 2007). Simple SDSMs disregard any residual noise term ε; whereas state-of-the-art SDSMs explicitly provide a noise model to represent variability and extremes. The former are often called deterministic, and the latter stochastic SDSM (van Storch, 1999a).

Typically, regression expressions (simple or multiple), stochastic processes (Hidden Markov Mode-HMM) and machine learning (artificial neural network ANN) methods are employed to construct the function F. A wide variety of combinations also exist, for instance, merging neural networks and clustering as proposed in this thesis, or merging analog methods and canonical correlation (e.g. Fern á ndez and S á enz, 2003). The SDSM downscaling methods are generally grouped into three categories (Wilby and Wigley, 1997; Wilby et al., 2004):

  • Regression models - statistical relationships are calculated between large-area and site-specific surface climate, or between large-scale upper air data and local surface climate (e.g., Li and Smith, 2009; Bergant and Kajfez-Bogataj, 2005).
  • Weather typing schemes - statistical relationships are determined between particular atmospheric circulation types and local weather (e.g., Hidalgo et al., 2008; Timbal et al., 2009; Yin et al., 2010).
  • Stochastic weather generators - these statistical models may be conditioned on the large-scale state in order to derive site-specific weather (e.g., Richardson and Wright, 1984; Semenov and Barrow, 1997).

Applying the transfer function F (Eq. 1.1) to predictors from numerical models in a weather forecasting context is justified if the predictors are realistically simulated, and thus, these methods are also known as perfect prognosis downscaling (e.g., Klein et al., 1959; Kalnay, 2003; Wilks, 2006). Even though SDSM does not incorporate any physical knowledge about the underlying relationship between the large- and regional-scale variables under consideration, the physical principles behind the relationship often can be identified from the statistical results by means of the spatial signatures of the anomalies. In this way, if the identified physical mechanism is plausible to remain unchanged in an altered climate, the SDSM will likely perform correctly under such altered conditions.

The development of an actual downscaling scheme generally involves two steps: 1) the selection of informative large-scale predictors and 2) the development of a statistical relationship between large-scale predictors and local-scale predictand (i.e., Eq. 1.1). The first step is almost equally important for SDSM as the second step, but few studies have systematically studied and included this step (e.g., Brinkmann, 2002; Cavazos and Hewitson, 2005; Hofer et al., 2010). In general, SDSM is based on the following three assumptions for suitable predictors (e.g., Benestad et al., 2008). The predictors must (1) have a physical relationship to the predictand, (2) be reliably represented by the reanalysis data or GCM, and (3) reflect climate change.

Often, the first step also requires transformation of the original predictors into a useful or interpretable form. This is because predictors are generally highdimensional fields of grid-based values. It is thus common to reduce the dimensionality of the predictor field and to decompose it into modes of variability.Possibly the most widely used multivariate statistical technique for dimensionality reduction in the atmospheric sciences is principal component analysis (PCA) (Preisendorfer, 1988; Hannachi et al., 2007). The technique became popular for analysis of atmospheric data following the research by Lorenz (1956), who called the technique empirical orthogonal function (EOF) analysis. Both names are commonly used, and refer to the same set of procedures (Wilks, 2006).PCA provides a set of orthogonally-based vectors (empirical orthogonal functions) to convert a data set containing a large number of variables into a data set containing fewer new variables. These new variables are linear combinations of the original ones, which are chosen to represent a large fraction of the variability contained in the original data (Huth, 1999). PCA, however, does not account for any information about the predictands, so that the predictor/predictand correlation might thus not be optimal. Different in this respect is canonical correlation analysis (CCA) or partial least square (PLS) analysis. This method identifies new variables that maximize the interrelationships between the predictor and the predictand field (e.g., Fernández and Sáenz, 2003; Bergant and Kajfez-Bogataj, 2005).

Another important aspect in selecting predictors is to determine an appropriate size of the spatial domain surrounding/near the downscaling target site (i.e., a grid or a station, even an area-averaged basin) (Wilby and Wigley, 2000; Timbal et al., 2009). This is because GCM outputs should not be seen as a true representation for a smaller-scale climate. The local processes represented as parameterization schemes in GCMs are important for the formation of the global climate only through their overall statistics, but not in terms of their details (von Storch, 1999b).Therefore, SDSM often is carried out at a certain spatial scope. There is no consensus on the choice of the most appropriate spatial domain. For example, Chu et al. (2010) carried out their downscaling at a domain with a single grid, while Hidalgo et al. (2008) took the whole USA continent as a downscaling domain. Based on previous studies, it can conclude that the optimum domain size highly depends on seasons, regions, selected predictors and downscaling methods underconsideration (Wilby and Wigley, 2000; Hewiston and Crane, 2006; Hidalgo et al.,2008; Timbal et al., 2009; Chu et al., 2010).

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Drawbacks

However, SDSM has drawbacks that need to be taken into account in its practical applications. First of all, an ideal SDSM needs a strong statistical relationship explaining completely the variability of the local-scale variable. This is never the case since the predictors never explain all of the variability of the local variable which is also affected by local factors not accounted for by the large-scale fields (Wilby et al., 2004; Hewitson and Crane, 2006; Fowler et al., 2007). Furthermore, these relationships are assumed to remain valid under future climate conditions (i.e., Stationarity) that may not always be justified, particularly for precipitation (Fowler et al., 2007). If climate change dynamically alters these physical processes relative to their present-day observed behavior, the statistical method will not be able to simulate these changes. On the other hand, it indicates that SDSM generally requires long-term observed historical time series to construct and validate the statistical relationship (Eq. 1.1). Additionally, the possible lack of reliability of the large-scale data generated by a GCM may affect the skill of SDSM, as it does to the dynamical approaches.

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Miscellaneous

There is no particular type of downscaling method that is absolutely superior to all others. Besides the above three categories of mainstream statistical downscaling methods, there are also other approaches employed.

With the increasing reliability and availability of RCM scenarios, recent work on statistical downscaling has aimed to combine the benefits of these two approaches (e.g., Pinto et al., 2010). That is to say, under the name model output statistics (MOS), gridded RCM simulations are statistically corrected and downscaled to point scales. Accordingly, an alternative classification for downscaling techniques was proposed by Rummukainen (1997) and was adapted by Maraun et al. (2010), who suggested to classify statistical downscaling approaches into perfect prognosis (PP; also referred to as “perfect prog”), MOS, and WGs. Generally, the PP consists of classical regression-based and weather-typing-based SDSMs, while MOS is also called statistical-dynamical downscaling approach (e.g., Pinto et al., 2010).

Scheme of different downscaling methods and their combinations (Yin, 2011)

MOS can be seen as a two-step procedure. It firstly uses the dynamical downscaling method to get regional climate information from GCM outputs. Next, these regional results are statistically downscaled to or are used to statistical bias correction (BC) procedure to attain grid-scale results (e.g., Ines and Hansen, 2006; Sharma, et al., 2007; Piani et al., 2009). Moreover, with more RCM scenarios available, the first step will be omitted and SDSMs will be directly applied to RCM outputs rather than GCM simulations in the future. Therefore, the core of MOS still belongs to the DDSM and SDSM family. The BC procedure mostly resembles a post-process procedure to fix the downscaling biases between downscaled and observed data. Certainly, it also can be directly used to GCM outputs termed as Bias Correction Spatial Downscaling (BCSD) (Wood et al., 2004; Maurer, 2007).

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How were climate change projections generated at regional and local scales? What are the pros and cons of the different methods?

In the context of downscaling, regional climate simulations offer the potential to include local phenomena affecting regional climate change that are not explicitly resolved in the global simulation. When incorporating boundary conditions corresponding to future climate, regional simulation can then indicate how these phenomena contribute to climate change.

There are three primary approaches to dynamical downscaling:

  • Limited-area models (Giorgi and Mearns 1991, 1999; McGregor 1997; Wang et al. 2004).
  • Stretched-grid models (e.g., Déqué and Piedelievre 1995; Fox-Rabinovitz et al. 2001, 2006).
  • Uniformly high resolution atmospheric GCMs (AGCMs) (e.g., Brankovic and Gregory 2001; May and Roeckner 2001; Duffy et al. 2003; Coppola and Giorgi 2005).

Limited-area models, also known as regional climate models (RCMs), have the most widespread use. The third method sometimes is called “time-slice” climate simulation because the AGCM simulates a portion of the period represented by the coarser-resolution parent GCM that supplies the model’s boundary conditions. All three methods use interactive land models, but sea-surface temperatures and sea ice generally are specified from observations or an atmosphere-ocean GCM (AOGCM). All three also are used for purposes beyond downscaling global simulations, most especially for studying climatic processes and interactions on scales too fine for typical GCM resolutions. As limited-area models, RCMs cover only a portion of the planet, typically a continental domain or smaller. They require lateral boundary conditions (LBCs), obtained from observations such as atmospheric analyses (e.g., Kanamitsu et al. 2002; Uppala et al. 2005) or a global simulation (with the consequence that the LBCs can “reign in” the behaviour of the RCM).

There has been limited two-way coupling wherein an RCM supplies part of its output back to the parent GCM (Lorenz and Jacob 2005). Simulations with observation based boundary conditions are used not only to study fine-scale climatic behaviour but also to help segregate GCM errors from those intrinsic to the RCM when performing climate change simulations (Pan et al. 2001). RCMs also may use grids nested inside a coarser RCM simulation to achieve higher resolution in subregions (e.g., Liang, Kunkel, and Samel 2001; Hay et al. 2006).

Stretched-grid models, like high-resolution AGCMs, are global simulations but with spatial resolution varying horizontally. The highest resolution may focus on one (e.g., Déqué and Piedelievre 1995; Hope, Nicholls, and McGregor 2004) or a few regions (e.g., Fox-Rabinovitz, Takacs, and Govindaraju 2002). In some sense, the uniformly high resolution AGCMs are the upper limit of stretched-grid simulations in which the grid is uniformly high everywhere.

Highest spatial resolutions are most often several tens of kilometers, although some (e.g., Grell et al. 2000a, b; Hay et al. 2006) have simulated climate with resolutions as small as a few kilometers using multiple nested grids. Duffy et al. (2003) have performed multiple AGCM time-slice computations using the same model to simulate resolutions from 310 km down to 55 km. Higher resolution generally yields improved climate simulation, especially for fields such as precipitation that have high spatial variability.

Some studies show that a higher resolution does not have a statistically significant advantage in simulating large-scale circulation patterns but does yield better monsoon precipitation forecasts and interannual variability (Mo et al. 2005) and precipitation intensity (Roads, Chen, and Kanamitsu 2003).

Improvement in results, however, is not guaranteed: Hay et al. (2006) find deteriorating timing and intensity of simulated precipitation vs. observations in their inner, high-resolution nests, even though the inner nest improves topography resolution. Extratropical storm tracks in a time slice AGCM may shift pole ward relative to the coarser parent GCM (Stratton 1999; Roeckner et al. 2006) or to lower-resolution versions of the same AGCM (Brankovic and Gregory 2001); thus these AGCMs yield an altered climate with the same sea-surface temperature distribution as the parent model.

Limitations of dynamical downscaling

Spatial resolution affects the computational effort required for a climate simulation because higher resolutions require shorter time steps to meet numerical stability and accuracy conditions. Higher resolutions in RCMs and stretched-grid models also must satisfy numerical constraints. Stretched-grid models whose ratio of coarse to-finest resolution exceeds a factor of roughly three are likely to produce inaccurate simulations due to truncation errors (Qian, Giorgi, and Fox-Rabinovitz 1999). Similarly, RCMs will suffer from incompletely simulated energy spectra and thus loss of accuracy if their resolution is more than 12 times finer than the resolution of the LBC source, which may be coarser RCM grids (Denis et al. 2002; Denis, Laprise, and Caya 2003; Antic et al. 2004, 2006; Dimitrijevic and Laprise 2005). In addition, these same studies indicate that LBCs should be updated more frequently than twice per day.

Even with higher resolutions than standard GCMs, models simulating regional climate still need parameterizations for subgrid-scale processes, most notably boundary-layer dynamics, surface-atmosphere coupling, radiative transfer, and cloud microphysics. Most regional simulations also require a convection parameterization, although a few have used sufficiently fine grid spacing (a few kilometres) to allow acceptable simulation without it (e.g., Grell et al. 2000). Often, these parameterizations are the same or nearly the same as those used in GCMs.

All parameterizations, however, make assumptions that they are representing the statistics of subgrid processes. Implicitly or explicitly, they require that the grid box area in the real world has sufficient samples to justify stochastic modeling. For some parameterizations such as convection, this assumption becomes doubtful when grid boxes are only a few kilometres in size (Emanuel 1994). The parameterizations for regional simulation may differ from their GCM counterparts, especially for convection and cloud microphysics. As noted earlier, regional simulation in some cases may have resolution of only a few kilometres, and the convection parameterization may be discarded (Grell et al. 2000).

Statistical downscaling

Statistical or empirical downscaling is an alternative approach for obtaining regional-scale climate information (Kattenberg et al. 1996; Hewitson and Crane 1996; Giorgi et al. 2001; Wilby et al. 2004, and references therein). It uses statistical relationships to link resolved behaviour in GCMs with the climate in a targeted area. The targeted area’s size can be as small as a single point. This approach encompasses a range of statistical techniques from simple linear regression (e.g., Wilby et al., 2000) to more-complex applications such as those based on weather generators (Wilks and Wilby, 1999), canonical correlation analysis (e.g., von Storch, Zorita, and Cubasch 1993), or artificial neural networks (e.g., Crane and Hewitson, 1998).

Empirical downscaling can be very inexpensive compared to numerical simulations when applied to just a few locations or when simple techniques are used. Lower costs, together with flexibility in targeted variables, have led to a wide variety of applications for assessing impacts of climate change. Some methods have been compared side by side (Wilby and Wigley 1997; Zorita and von Storch 1999; Widman, Bretherton, and Salathe 2003). These studies have tended to show fairly good performance of relatively simple vs. more-complex techniques and to highlight the importance of including moisture and circulation variables when assessing climate change. Statistical downscaling and regional climate simulation also have been compared (Kidson and Thompson 1998; Mearns et al. 1999; Wilby et al. 2000; Hellstrom et al. 2001; Wood et al. 2004; Haylock et al. 2006), with no approach distinctly better or worse than any other. Statistical methods, though computationally efficient, are highly dependent on the accuracy of regional temperature, humidity, and circulation patterns produced by their parent global models. In contrast, regional climate simulations, though computationally more demanding, can improve the physical realism of simulated regional climate through higher resolution and better representation of important regional processes. The strengths and weaknesses of statistical downscaling and regional modeling thus are complementary.

A summary of the primary strengths and weaknesses of statistical and dynamical downscaling, or regional climate modelling
Statistical Downscaling Dynamic Downscaling

Strengths

Computationally efficient

Requires only monthly or daily GCM output

Can relate GCM output directly to impact-relevant variables not simulated by climate models

Explicitly consists of both large-scale and small-scale physical processes, up to the resolution of the model

Regional climate response is consistent with global forcing

Can be applied to any consistently- observed variable

Can provide site-specific estimations

Provides data that is coherent both spatially and temporally and across multiple climate variables

Can be used to generate a large number of realizations in order to quantify uncertainty

Can be used in regions where no observations are available

Weakness

Based on the essentially unverifiable assumption that statistical relationships between predictors and predictands remains stationary under future change

Assumes that sub-grid parameterization schemes remain stationary in the altered climate

Sensitive to choice of predictors and GCM ability to simulate these predictors

Sensitive to initial boundary conditions from GCMs

Tends to underestimate temporal variance

Requires long-term observed data

Highly computationally demanding

Difficulty to generate multiple scenarios

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