- Introduction
- Principles in Empirical Downscaling
- Weather generators
- Transfer functions
- Weather typing
- Temporal variance
- Validation
- Comparison of downscaling methodologies
- Predictors in statistical/empirical downscaling
- Comparison of dynamical and empirical downscaling methods
- Uncertainty
Coupled AOGCMs are the modeling tools traditionally used for generating projections of climatic changes due to anthropogenic forcing. However, due to limited computational resources, the horizontal resolution of present day coupled AOGCMs is still of the order of a few hundred km. At this resolution, the effects of local and regional physiographic detail, like land-sera distribution, topography and land-se on regional climate is not fully captured. Therefore, a number of techniques have been developed to enhance the regional information provided by coupled AOGCMs The basic objective of these regionalization techniques is to enhance the regional information provided by coupled AOGCMs by combining consistently large-scale climatic information with effects of small scale physiographic detail. In this contribution we review the state of the art of empirical downscaling.
A number of review papers have dealt with downscaling concepts, prospects and limitations: von Storch (1995), Hewitson and Crane (1996), Wilby and Wigley (1997), Gyalistras et al. (1998), and Murphy (1999a,b). A more up-to-date review, including dynamical regionalization techniques based on high resolution time slice GCM simulations and regional climate models, is presently under preparation for the Third Assessment Report of the IPCC.
"Downscaling" is based on the view that regional climate is conditioned by climate on larger, for instance continental or even planetary, scales (von Storch, 1995, 1999a). Information is cascaded "down" from larger to smaller scales. The regional climate is the result of interplay of the overall atmospheric, or oceanic, circulation and of regional specifics, such as topography, land-sea distribution and land-use. As such, empirical/statistical downscaling seeks to derive the local scale information from the larger scale through inference from the cross-scale relationships, using some a random or deterministic function f such that:
local climate response = f (external, larger scale forcing)
The concept of "downscaling" does not imply that the regional climate would be determined by the large-scale state; for similar large-scale states, the associated regional states may vary substantially (Starr, 1942; Roebber and Bosart, 1998). Instead, the regional climate is seen as a random process conditioned upon a driving large-scale climate regime. Of course, one could challenge this view since the small scales undoubtedly have an effect on the large scales as well, and that a proper regionalization should describe the mutual influence of large scales on small scales and vice versa. However, the effect of small scales on large scales is not limited to specific region, but all regions exert this influence. That is, one would have to model all regions, resulting in a global model of increased resolution everywhere. This strategy is pursued in high-resolution time slice simulations, but the computational load makes it inaccessible in most applications. Also, the effect of sub-grid scale influences on the large scales resolved in AOGCMs is taken care of in a summary, statistical manner by parameterizations (von Storch, 1998).
Downscaling is not really a new approach, even though it is used in a new context, namely specifying expected regional and local climate variations and change. Similar techniques were used in the past decades for deriving finer-scale (local) weather information from numerical weather prediction models - called Perfect Prog (Klein and Glahn, 1974) - and for classifying weather regimes (Großwetterlagen; e.g., Baur et al., 1944; Lamb 1972).
The conceptual approach lends itself to (relative) computational simplicity, and is thus attractive in situations where the resources for dynamical models are not available, or where a dynamical model does not explicitly model the predictand of interest. As a result a plethora of downscaling applications have been developed, and while there is methodological similarity, the permutations are diverse to the point of making inter-comparison of the climate change results from separate studies difficult, if not impossible.
The confidence that may be placed in downscaled climate change information is foremost dependent on the validity of the large-scale fields from the GCM. Since different variables have different characteristic spatial scales, some variables are considered more realistically simulated by GCMs than others. For instance, derived variables (not fundamental to the GCM physics, but derived from the physics) such as precipitation are usually not considered as robust information at the regional and grid scale (e.g., Osborn and Hulme, 1997; Trigo and Palutikof, 1999). Conversely, tropospheric quantities like temperature or geopotential height are intrinsic parameters of the GCM physics and are more skillfully represented by GCMs. However, there is no consensus in the community about what level of spatial aggregation (in terms of number of grid cells) is required for the GCM to be considered skillful. For example Widmann and Bretherton (2000) find monthly precipitation on spatial scales of three grid lengths (in their case: 500 km) reliably simulated.
An interesting by-product of empirical downscaling approaches is that they offer a straightforward method of testing GCMs' ability in simulating regional and local details. Specifically, are they able to reproduce the empirically found links between large-scale and small-scale climate (Busuioc et al., 1999; Murphy, 1999a; Osborn et al., 1999).
Formally, the concept of regional climate being conditioned by the large-scale state may be written as
R = F(L)
Here, R represents the predictand (a set of regional climate variables), L is the predictor (a set of large-scale variables), and F a stochastic and/or deterministic function conditioned by L. In general, F is unknown and is modeled dynamically (i.e., through regional climate models) or empirically from observational (or modeled) data sets. In some cases R and L are the same variables but on different spatial scales (for example the disaggregation schemes of Bürger, 1997; Wilks, 1999b; and Widmann and Bretherton, 2000).
Note that the formulation R=F(L) implies that the variation of the regional or local variable may be displayed in a phase space spanned by L. This view is demonstrated in Figure 1, displaying different fits of F, with linear regression, kriging, neural nets and the analog technique, for the case of local monthly precipitation amounts as a function of monthly air pressure configurations (von Storch, 1999b).
When using downscaling for assessing regional climate change, three implicit assumptions are made:
(1) The predictors are variables of relevance and are realistically modeled by the AOGCM.
(2) The transfer function is valid also under altered climatic conditions. This is an assumption that in principle can not be proven in advance. The observational record should cover a wide range of variations in the past; ideally, all expected future realizations of the predictors should be contained in the observational record.
(3) The predictors employed fully represent the climate change signal.
A diverse range of downscaling techniques methods has been developed, but in principle fall into three categories:
(a) Weather generators, which are random number generators of realistically looking sequences conditioned upon the large-scale state.
(b) Transfer functions, where a direct quantitative relationship is derived through, for example, regression.
(c) Weather typing schemes based on the more traditional synoptic climatology concept (including analogs and phase space partitioning) and which relate a particular atmospheric state to a set of local climate variables.
Figure 1: Different approximations of the "surface" R = F(L), with R being monthly mean winter precipitation at a location in Northern Spain, and L given by the principal components (EOF coefficients) of North Atlantic/European monthly mean air pressure fields. The F-surface is approximated by Canonical Correlation Patterns (i.e., by a linear plane), by kriging (i.e., weighted interpolation), by analogs (nearest neighbors) and by an artificial neural network. (von Storch, 1999b)
Most downscaling applications have dealt with temperature and precipitation. However, a wide array of studies exists in which other variables have been investigated. The forthcoming IPCC report features a table with various applications, their methods, predictand variables and regions.
Weather generators are statistical models of observed sequences of weather variables. They can also be regarded as complex random number generators (Katz and Parlange, 1996), the outputs of which resemble daily weather data at a particular location (Wilks and Wilby, 1999). There are two fundamental types of daily weather generators, based on the approach to modeling daily precipitation occurrence: the Markov chain approach (e.g., Richardson, 1981; Hughes et al., 1993, Lettenmaier, 1995; Hughes et al., 1999) and the spell-length approach (Racksko et al., 1991; Wilks, 1999a). In the Markov chain approach, a random process is constructed which determines a day at a station as rainy or dry, conditional upon the state of the previous day, following given probabilities. If a day is determined as rainy then the amount is drawn from a probability distribution (Lettenmaier, 1995). Wilks (1999a) and Semenov et al. (1998) compare these methods.
For statistical downscaling the parameters of the weather generator are conditioned upon a large-scale state (see Katz and Parlange, 1996; Wilks, 1999a; Wilby et al., 1998; Charles et al., 1999a), or relationships can be developed between large-scale parameters sets of the weather generators and local scale parameters (Wilks, 1999b). Conditioning on large-scale states alleviates one of the chronic flaws of many weather generators, which is the underestimation of interannual variations of the weather variables (Wilks, 1989), and, to a degree, induces spatial correlation (Hughes and Guttorp, 1994).
The more common approaches found in the literature are regression-like techniques or piecewise interpolations using a linear or nonlinear formulation. The simplest approach is to build multiple regression models relating free atmosphere grid point values to surface variables. For example Sailor and Li (1999) have in this manner modeled local temperature at a series of US stations. Other regression models use field of spatially distributed variables to specify local temperatures in Sweden (e.g., Chen et al., 1999), or principal components of regional geopotential height fields (e.g., Kidson and Thompson, 1998, Hewitson and Crane, 1992).
Canonical Correlation Analysis (e.g., von Storch and Zwiers, 1999) has found wide application. A variant of CCA is redundancy analysis, which is theoretically attractive as it maximizes the predictands variance; however, in practical terms it seems similar to CCA (WASA, 1998). Also Singular Value Decomposition has been used (Huth, 1999), which is another variant of CCA.
Most applications have dealt with precipitation; for instance Busuioc and von Storch (1996) and Busuioc et al. (1999) with Rumanian monthly precipitation amounts, or Dehn and Buma (1999) with a French Alpine site. Kaas et al (1996) have successfully specified local pressure tendencies, as a proxy for local storminess, from large-scale monthly mean air pressure fields. Another application was by Fischlin and Gyalistras (1997) for the Alps.
Oceanic climate and climate impact variables have also been dealt with: salinity in the German Bight (Heyen and Dippner, 1998); and salinity and oxygen in the Baltic (Zorita and Laine, 2000); sea level (Cui at al., 1996; Cui and Zorita, 1998; Heyen et al., 1996); and a number of ecological variables such as abundance of species (Kröncke et al., 1998; Heyen et al., 1998, Dippner, 1997a,b). In addition statistics of extreme events, expressed as percentiles within a month or season, have been modeled: storm surge levels (von Storch and Reichardt, 1997; Langenberg et al., 1999) and ocean wave heights (WASA, 1998).
An alternative to linear regression is to use piecewise linear or nonlinear interpolation; geostatistics offers elegant "kriging" tools to this end (e.g., Wackernagel, 1995). The potential of this approach has been demonstrated by Biau et al. (1999), who related local precipitation to large-scale pressure distributions. Another approach is to use cubic splines, as is done by Buishand and Klein Tank (1996), Brandsma and Buishand (1997) and Buishand and Brandsma (1999) for specifying precipitation.
Another non-linear approach is based on artificial neural networks (ANN), which are generally more powerful than other techniques, although the interpretation of the dynamical character of the relationships is less easy. For example, Trigo and Palutikof (1999) map with an ANN SLP and 500 hPa height values on daily temperature at a station in Portugal and find significantly improved specification as compared to a linear ANNs. Other applications of ANN have successfully been implemented by Hewitson and Crane (1996), Cavazos (1997, 1999), Wilby et al. (1998), Crane and Hewitson (1998), McGinnis (1994), and Weichert and Bürger (1998).
The synoptic downscaling approach empirically defines weather classes related to local and regional climate variations. These weather classes may be defined synoptically or fitted specifically for downscaling purposes by constructing indices of airflow (Conway et al., 1996). The mean, or frequency, distributions of local or regional climate are then derived by weighting the local climate states with the relative frequencies of the weather classes. Climate change is then estimated by determining the change of the frequency of weather classes.
In many cases, the local and regional climate states are derived from the observational record. Wanner et al. (1997) used changing global to continental scale synoptic structures for understanding and reconstructing Alpine climate variations, while Widmann and Schär (1997) could not relate changing Swiss precipitation to changing statistics of weather classes. Kidson and Watterson (1995) made a similar analysis for New Zealand. Enke and Spekat (1997) offer other applications, while Goodess and Palutikof (1998) and Wilby (1998). Jones and Davies (1999) apply the technique for studying changing air pollution mechanisms.
In the "statistical/dynamical" approach, meso-scale atmospheric models are utilized for simulating a series of typical weather states. The advantage over the former technique is that in this way spatially distributed local climates are specified. The technique has been named statistical-dynamical. Its feasibility has been demonstrated by a series of studies on climate and climate change in the Alps: Frey-Buness et al. (1995), Fuentes and Heimann (1996), Fuentes et al. (1998), Heimann and Sept (1999).
The analog method was introduced into the downscaling context by Zorita et al (1995) and recently reviewed by Zorita and von Storch (1999); its applicability was demonstrated by Cubasch et al. (1996), Martin et al. (1997), Biau et al. (1999) and Dehn (1999), mostly for the specification of daily precipitation. Conceptually similar, but mathematically more demanding are techniques which partition the large-scale state phase space, for instance with Classification Tree Analysis, and use a randomized design for picking regional distributions. This technique was pioneered by Hughes et al (1993), and further developed by Zorita et al. (1995) and Schnur and Lettenmaier (1999). Lettenmaier (1995) gives a general overview of these techniques. Both analog and CART approaches return the right level of variance and correct spatial correlation structures.
Transfer function approaches and some of the weather typing approaches suffer to varying degrees from an under-prediction of temporal climate variability, since only part of the regional and local temporal variability of a climate variable is related to large scale climate variations, while another part is generated regionally. (For the case of regression the mathematics of this principle are worked out by Katz and Parlange (1996)). Two approaches for bringing the downscaled climate variables to the right level of variability are in use: inflation and randomization. In the inflation approach, originally suggested by Karl et al. (1990), the variation is increased by the multiplication of a suitable factor; a more sophisticated approach, named "expanded downscaling", was developed by Bürger (1996). It is a variant of Canonical Correlation Analysis that ensures the right level of variability. This approach is utilized by Huth (1999) and Dehn et al. (2000). In the randomization approach the unrepresented variability is added as unconditional noise; that is, in the simplest case, the "missing" variance is added in the form of white noise (Kilsby et al., 1998; Hewitson, 1998). The concept is worked out in von Storch (2000), and applications are offered by Dehn and Buma (1999) and Buma and Dehn (1998).
The validation of downscaling techniques is essential but difficult. It requires demonstrating the robustness of the downscaling under future climates, and that the predictors used represent the climate change signal. Both assumptions are not possible to rigorously test, as no empirical knowledge is available so far. The analysis of historical developments as well as simulations with GCMs can provide support for these assumptions.
The classical validation approach is to specify the downscaling technique from a segment of available observational evidence and then assess the performance of the empirical model by comparing its predictions with independent observed values. This approach is particularly valuable when the observational record is long and documents significant changes in the course of time. An example is the analysis of absolute pressure tendencies in the North Atlantic by Kaas et al. (1996), who fitted a regression model which related spatial air pressure patterns to pressure tendency statistics. Using data from the most recent decades they successfully reproduced the considerably stormier times earlier this century. Similarly Wilks (1999) developed a downscaling function on dry years and found it functioning well in wet years. However, the success of a statistical downscaling technique for representing present day conditions does not imply legitimacy for changed climate conditions (Charles et al., 1999b).
An alternative approach is to use a series of comparisons between models and transfer functions, as demonstrated by Busuioc et al (1999) and Charles et al. (1999b). In the former study, it was first demonstrated that the GCM incorporated the empirical link; in the latter, a regional climate model was used. From these findings it was concluded that the dynamical models would correctly "know" about the empirical downscaling link; then the climatic change, associated with a doubling of carbon dioxide, was estimated through the empirical link and compared with the result of the dynamical model. In both cases, the dynamical response was found to be consistent with the empirical link, indicating the validity of the empirical approach and its legitimate approach in downscaling other global climate change information.
There is a paucity of systematic studies that use common data sets applied to different procedures over the same geographic region. A number of articles discussing different empirical and dynamical downscaling approaches (Giorgi and Mearns, 1991; Hewitson and Crane, 1996; Wilby and Wigley, 1997; Buishand and Brandsma, 1997; Rummukainen, 1997; Zorita and von Storch, 1997; Gyalistras et al., 1998; Kidson and Thompson, 1998, Murphy, 1999b) do present summaries of the relative merits and shortcomings of different procedures. These intercomparisons vary widely with respect to predictors, predictands and measures of skill. A systematic, internationally coordinated intercomparison project would be useful.
The most systematic and comprehensive study so far is that one by Wilby et al. (1998) and Wilby and Wigley (1997). They compared empirical transfer functions, weather generators, and circulation classification schemes over the same geographical region using climate change simulations and observational data. The study considered a demanding task to downscale daily precipitation for six locations over North America, spanning arid, moist tropical, maritime, mid-latitude, and continental climate regimes. A suite of 14 measures of skill was used, strongly emphasizing daily statistics. These included such measures as wet spell length, dry spell length, 95th percentile values, wet-wet day probabilities, and several measures of standard deviation. Downscaling procedures in the study included two different weather generators, two variants of an ANN-based technique, and two stochastic/circulation classification schemes based on vorticity classes.
The results prove to be illuminating, but require careful evaluation as they are more indicative of the relative merits and shortcoming of the different procedures, rather than a recommendation of one procedure over another. In the validation phase of the study the downscaling results were compared against the observational data, and indicated that the weather generator techniques were superior to the stochastic/circulation classification procedures, which in turn were superior to the ANNs. However, the superiority of the weather generator when validated against the observed data is misleading as the weather generators are constrained to match the original data perfectly. Similarly, the improved performance of the circulation classification techniques with regard to the ANNs is largely a reflection of the measures of skill used and indicates the tendency of ANNs to over-predict the frequency of trace rainfall days. In contrast, when the inter-annual attributes of monthly totals are examined the performance ranking of the techniques is approximately reversed with the weather generators performing especially poorly.
The results indicate strength by weather generators to capture the wet-day occurrence and the amount distributions in the data, but less success at capturing the inter-annual variability (the low frequency component). The important question with this procedure is thus how to perturb the weather generator parameters under future climate conditions. At the other end of the spectrum the ANN procedures performed well at capturing the low frequency characteristics of the data, and showed less ability at representing the range of magnitudes of daily events. The stochastic/circulation typing schemes, being somewhat a combination of the principles underlying weather generators and ANNs, appear to be a better all-round performer.
In application to GCM simulations of future climate, the procedures showed some consistency with the ANN indicating the largest changes in precipitation. However, assessing the relative significance of the changes is non-trivial, and at this level of inter-comparison the results of the climate change application are perhaps more useful in a diagnostic capacity of the GCM which appeared to show differences in the strength of the precipitation-circulation relationship.
What is not evaluated in this study to any great degree is the range of variance spanned by each technique. Addressing this issue Wilby et al. (1998) and Conway et al. (1996) apply transfer functions to determine wet/dry probabilities and then use a stochastic procedure for the magnitude of precipitation, and in doing so capture some degree of the low frequency and high frequency variance. Zorita et al. (1995) and later Cubasch et al. (1996) demonstrated that a suitably designed analog technique reproduces storm interarrival terms well.
An additional factor not yet fully evaluated in any comparative is that of the temporal evolution of daily events. In this respect the manner in which daily events develop may be critical in some areas of impacts analysis, for example hydrological modeling. While a downscaling procedure may correctly represent, for example, the number of rain days, the temporal sequencing of these may be as important.
A final point to note with regard to different techniques, is that of the relative merits of non-linear and linear approaches. For example, Conway et al. (1996) and Brandsma and Buishand (1997) use circulation indicators as predictors and note that the relationships with precipitation on daily time scales are often non-linear. Similarly Corte-Real et al. (1995) effectively applied multivariate adaptive regression splines (MARS) to approximate non-linearity in the relationships between large-scale circulation and monthly mean precipitation. However, the application of MARS to large volume daily data may be more problematic.
It thus appears that downscaling of the short-term climate variance benefits from the use of more flexible models, as long as enough empirical evidence is available for avoiding overfitting. In particular, downscaling of daily precipitation benefits appreciably from the ability to better capture convective events, while for longer time scales the advantage of higher flexibility is getting less (Biau et al., 1999; von Storch, 1999b).
Most of the comparative studies mentioned above come to the conclusion that techniques differ in their success of specifying regional climate, and the relative merits and shortcomings emerge differently in different studies. This is not surprising, as there is considerable flexibility in setting up a downscaling procedure, and the suitability of a technique and the adaptation to the problem at hand varies.
The list of predictands in the literature is very broad and comprise direct climate variables (e.g.: precipitation, temperature, salinity, snow pack), monthly or yearly statistics of climate variables (distributions in wind speeds, wave heights, water levels, frequency of thunderstorm statistics), as well as impacted variables (e.g.: frequency of land slides). Useful summaries of downscaling techniques and the predictors used are also presented in Rummukainen (1997), Wilby et al. (1998) and Wilby and Wigley (1997).
However, outside of passing references in many studies to the effect that a range of predictors were evaluated, there is little systematic work that has explicitly evaluated the relevant skill of different atmospheric predictors (Winkler et al., 1997). The one commonality between most studies is, not surprisingly, the use of some indicator of the large-scale circulation.
The choice of the predictor variables is of utmost importance. For example, Hewitson (1997, 1998) has demonstrated how the downscaled scenario of future change in precipitation may alter significantly depending on whether or not humidity is included as a predictor. The implication here is that while a predictor may or may not appear as the most significant when developing the downscaling function under present climates, the changes in that predictor under a future climate may be critical for determining the climate change.
A similar critical issue exists with respect to downscaling temperature. Werner and von Storch (1993) and Schubert (1998) documented that changes of local temperature may not be driven by circulation changes alone, but may be dominated by changes in the radiative properties of the atmosphere. This is a particular vulnerability of any downscaling procedure in light of the propensity to use circulation predictors alone that do not necessarily reflect the changed radiative properties of the atmosphere.
One possible solution is to incorporate the large-scale temperature field from the GCM as a surrogate indicator of the changed radiative properties of the atmosphere. This approach has been adopted by Dehn and Buma (1999) in their scenario of future Alpine land slides. Another solution is to use several large-scale predictors, such as gridded temperature and circulation fields (e.g., Gyalistras et al., 1998; Huth, 1999).
After the availability of homogeneous re-analyses (Kalnay et al., 1996), the number of candidate predictor fields has been greatly enhanced; earlier, the empirical evidence about the c-variability of regional/local predictands and large-scale predictors was very limited and made many studies choose either gridded near surface temperature or air pressure, or both. These "new" data sets will allow significant improvements in accuracy of empirical downscaling techniques.
Few formal comparative studies of different regionalization techniques have been carried out. To date, published work mostly focused on the comparison between regional climate model and statistical downscaling techniques.
Kidson and Thompson (1998) used the RAMS dynamical model to downscale reanalysis data (ECMWF) over New Zealand to a grid resolution of 50km. The statistical downscaling used a screening regression technique to predict local minimum and maximum daily temperature, and daily precipitation. The regression technique limits each regression equation to 5 predictors (selected from EOFs of 1000hPa and 500hPa geopotential height fields, local scalar wind speed and anomalies of geostrophic wind speed at 500hPa and 1000 hPa, anomalous 1000hPa-500hPa thickness and relative vorticity, and terms of vorticity advection). The results indicated little difference in skill between the two techniques, and Kidson and Thompson suggest that, subject to the assumption of statistical relationships remaining viable under a future climate, the computational requirements do not favor the use of the dynamical model, although it is noted that the dynamical model performed better with convective components of the precipitation.
Murphy (1999a,b) found similar levels of skill for present day climate for the dynamical and statistical methods, in line with the Kidson and Thompson (1998) study. The statistical method was nominally better for summertime estimates of temperature, while the dynamical model gave better estimates of wintertime precipitation. However, unlike the validation study which compared the downscaling against observational data, the climate change situation showed larger differences between the statistical and dynamical techniques. The study concludes that the differences in the temperature downscaling do not derive from a breakdown of the statistical relationships, as might be suspected, but are perhaps related to different predictor/predictand relationships in the GCM. In contrast, the downscaled precipitation differences may stem from the exclusion of specific humidity in the regression equation, as moisture was a weak predictor of the natural variability. This point would seem to confirm the humidity issue raised above (Hewitson, 1997, 1998).
Mearns et al. (1999) also compared regional model simulations and statistical downscaling, in this case using the RegCM2 regional model, and a semi-empirical technique whereby stochastic procedures are conditioned on weather types classified from circulation fields (700hPa geopotential heights). While Mearns et al. suggest that the semi-empirical approach incorporates more physical meaning into the relationships, this approach does impose the assumption that the circulation patterns are robust into a future climate in addition to the normal assumption that the cross-scale relationships are stationary in time. For both the techniques the driving fields are from the CSIRO GCM to downscale daily temperature and precipitation over central-northern USA (Nebraska). As with the preceding studies, the validation under present climate conditions indicated similar skill levels for the dynamical and statistical approaches, with some advantage by the statistical technique.
Also in line with the Murphy (1999a,b) study, larger differences were noted when climate change scenarios were produced. Notably for temperature, the statistical technique produced an amplified seasonal cycle compared to both the RegCM2 and CSIRO data, although similar changes in daily temperature variances were found in both RegCM2 and the statistical technique (with the statistical approach producing mostly decreases). The spatial patterns of change showed greater variability with RegCMs2 compared to the statistical technique. Mearns et al. suggest that some of the result differences are due to the climate change simulation exceeding the range of data used to develop the statistical model, while the decreases in variance are likely a true reflections of changes in the circulation controls.
The precipitation results from Mearns et al. are in contrast to earlier studies, and the RegCM2 produced few statistically significant changes (although both increases and decreases were indicated), whereas almost half the changes derived from the statistical technique (almost always an increase) were statistically significant.
Overall, the above comparative studies indicate that under the present climate both the dynamical and empirical techniques have similar skill. The question arise as to which is "more correct" under future climates. While the dynamical model should clearly provide a better physical basis for change, it is still unclear whether different regional models generate similar downscaled changes, and whether the computational cost relative to statistical/empirical techniques is merited.