The MACA method is a statistical method for downscaling Global Climate Models (GCMs) from their native coarse resolution to a higher spatial resolution that captures both the scales relevant for impact modelling while preserving time-scales and patterns of meteorology as simulated by GCMs (See short lecture videos on statistical downscaling and MACA). This method has been shown to be slightly preferable to direct daily interpolated bias correction in regions of complex terrain due to its use of a historical library of observations and multivariate approach (Abatzoglou and Brown, 2011). Variables that are downscaled include 2-m maximum/minimum temperature, 2-m maximum/minimum relative humidity, 10-m zonal and meridional wind, downward shortwave radiation at the surface, 2-m specific humidity, and precipitation accumulation all at the daily timestep.

John discusses the basics of statistical downscaling methods, inclusding the simplest of methods.

Uploaded on Mar 3, 2011

John discusses the more advanced statistical downscaling methods, such as constructed analogs

Uploaded on Mar 3, 2011

John discusses dynamical downscaling methods such as regional climate models and some applications
of downscaled data to look at fire.

Uploaded on Mar 3, 2011

Both GCM data and observation data are interpolated to a common 1 degree grid in latitude/longitude.

The seasonal and yearly trends at each grid point are calculated using a 21-day, 31-year running mean of the data and removed. This trend is replaced as the final step in MACA.This step helps to avoid the lack of suitable weather analogs in a changing climate.

At each grid point, the cumulative distribution function (CDF) of a 15-day window and all years of data(historical or future) is considered for both the GCM data and the observation data. The bias correction step maps the CDF of the historical GCM data and the future GCM data to the CDF of the observation data using a non-parametric quantile-mapping method. To avoid stationarity in distributions of future model runs, quantile differences between the historical and future GCM data are preserved after the bias correction step. This bias correction is applied first to coarse GCM data and secondly to the fine GCM data after the Constructed analogs step. This method is the Equidistant Quantile Mapping (EDCDFm,Li et al., 2010) method which preserves additive future differences for temperature, but unlike that method preserves multiplicative future ratios for precipitation.

A best fit approach is applied to a daily *target* GCM data by identifying days in our observation record that had similar, or analogous, spatial patterns for a suite of variables. The procedure as adapted from Hidalgo (2008) identifies the top 100 patterns of observed meteorological variables (e.g., tmax and tmin) that occurred no-more than 45 days from the day of year for the *target* GCM day. With over 30 years of data, this allows us to select the best 100 out of over 900 historical days. Patterns are selected based on the lowest root-mean-square error (RMSE) to the *target* pattern. Rather than only using a single "best" analog, the constructed analog approach uses a superposition of the top patterns through matrix inversion that allows us to estimate coefficients for each pattern that can then be used to develop a linear model for the target day. The same
coefficients in this superposition are also applied to the fine observation data and superposed to create the downscaled GCM data.

For variables epoch adjusted in step #2, epoch adjustments are reintroduced to ensure consistency with GCM data.

Using the same procedure as detailed above, results of the constructed analogs are bias corrected to ensure compatability with the observational dataset.

- In v2, the trend in all variables is removed at the start.

- In v1, the trend for only tasmax/tasmin,uas/vas was removed at the start.

- In v2, the trend is removed for both the historical and future periods.

- In v1, the trend was only removed in the future period.

- In v2, after the coarse bias correction of the multiplicative variables (i.e. pr, huss,wind speed), the trend is removed again (as the coarse bias correction can modify this trend).

- In v2, we use 10 patterns.

- In v1, we use 100 patterns(there may be some overfitting here).

- In v2, we interpolate the error in the constructed coarse pattern and add it to the constructed downscaling at the fine level.

- In v1, we throw away the coarse error from the constructed analogs method.

- In v2, we bias correct pr,huss,rsds independently, but bias correct tasmax and tasmin jointly with the corrected precipitation.

- In v1, we bias correct all variables indpendently.