The statistical downscaling method is an extension of the downscaling described in Timm and Diaz (2009). The statistical downscaling in that study can be sectioned into three parts:

- Diagnostic studies of the present-day circulation-rainfall relation
- Developing a linear regression model
- Application the derived regression model to future climate change scenarios

The goal is to identify climate circulation anomalies over the North Pacific and tropical Pacific that have a controlling influence on the local rainfall variations in Hawai‘i. We extended the analysis to take vertical stability and moisture transport into account (see Table 1.) NCEP-I reanalysis data are used in this study from 1978-2007.

Label |
Description |

zg500 |
500 hPa geopotential heights |

zg1000 |
1000 hPa geopotential heights |

ta1000-500 |
Temperature difference 1000hpa -500hPa |

hus-uwnd-700 |
Zonal moisture transport in 700hPa |

hus-vwnd-700 |
Meridional moisture transport in 700 hPa |

The local rainfall data is the latest compilation from the Rainfall Atlas of Hawai‘i (Giambelluca *et al*., Bull. Amer. Meteor. Soc*.*, 2012,doi: 10.1175/BAMS-D-11-00228.1). The monthly mean gap-filled station data are used with a total number of stations of n=1104. We refer to the large-scale climate fields as a time-dependent vector *X(t)* and the rainfall at a selected station as *y(t),* where *t* refers to a specific year. Note that for Hawai‘i we analyze the wet (November of year (*t-1)’* – April of year *t*) and dry (May-October of year *t*) seasons.

The statistical method is based on the concept of ‘compositing’ the large-scale climate variables into subsets of years with high and low rainfall at a given single station. The composite-technique is measuring the covariability of the large-scale circulation with the local rainfall anomalies in two categories: rainfall above the approximate 80% quantile and below the 20%-quantile. Here we use the years 1978-2007 seasonal mean data (for the 31 years sample we therefore use 6 lowest and 6 highest rainfall seasons). The high and low rainfall samples of *X(t)* are averaged and the climatological mean (1978-2007) is subtracted from the composite means, resulting in average circulation anomalies associated with high and low rainfall seasons (*F+*, *F-,* respectively). These patterns serve as templates for the statistical downscaling of the reanalysis data and later for the CMIP5 model scenario simulations. We obtain for each climate variable a projection index that measures the similarity between a given circulation anomaly of a season in year t with the composite anomaly pattern. Mathematically the circulation anomalies and composite pattern can be represented in vectors and the standard vector projection is used here as a similarity index (note that the projection index measures both, the spatial correlation and the magnitude of the anomalies).

*i+(t) = <C(t), F+>/ *|| *F+* ||

*i-(t) = <C(t), F->/ *|| *F-* ||

where <,> is the vector scalar product and || || denotes the length of the vector.

The statistical downscaling (SD) follows the same principle as in our previous study and deploys linear regression to a multiple predictor set. For the calibration period 1978-2007 the reanalysis fields (all fields are anomalies with respect to the climatological mean 1978-2007) are projected onto the composite pattern. For each station we obtain 10 large-scale climate predictor time series (5 variables [Table 1] and 2 composites [high and low rainfall] that carry information about the station’s precipitation anomaly). Note that seasonal precipitations are expressed as relative changes to the climatological mean [units %].

Since the number of rainfall stations has significantly increased compared to the earlier SD studies, we conducted Principal Component Analysis (PCA) on the projection time series before fitting the MLR regression model for the individual stations. This step serves as a data compression method and regularization of the single-station composite technique. It captures the major modes of large-scale climate variability and translates them into regional rainfall anomaly pattern, albeit with limited spatial degrees of freedom.

The CMIP5 data archive provides access to collection of climate change model simulations with standardized model scenarios for anthropogenic climate forcing. Historical runs (simulations beginning in the preindustrial climate of the mid 19th century to present (A.D. 2006) and two representative concentrations pathways (RCPs) were analyzed: RCP4.5 and RCP8.5 which result in a radiative forcing of 4.5Wm^{-2} and 8.5Wm^{-2} by 2100, respectively. We used a total of 32 models to perform the statistical downscaling. Note that we used only one scenario simulation from each model.

For each model scenario simulation the monthly mean climate variables were extracted and preprocessed to form seasonal mean values. The fields were projected onto the composite pattern and the resulting projection index times passed through the PCA filter. For each model the resulting predictor time series were standardized using the 1975-2005 historical scenario model years. These standardized predictor time series were used then to estimate the rainfall anomalies for years 2041-2071 in the RCP scenarios using the fitted regression parameters.

The results presented on the maps show the estimated rainfall changes during the mid 21st century (model years 2041-2071) in percent of the present-day climatological seasonal rainfall amount (1978-2007) at each station. We currently provide the wet season (November-April) results. The shown values represent the median of the multi-model ensemble results. Further information is given in the info boxes for each station including the multi-model ensemble standard deviation, and 25% and 75% quantiles from the multi-model ensemble.

**Citation:**

Oliver Elison Timm, Thomas W. Giambelluca and Henry F. Diaz: Statistical Downscaling of Rainfall Changes in Hawai‘i based on the CMIP5 Global Model Projections, *Journal of Geophysical Research – Atmospheres*, in review, 2014.

Additional information on the statistical downscaling approach can be found in:

Timm, O. and H. F. Diaz, 2009: Synoptic-Statistical Approach to Regional Downscaling of IPCC 21st Century Climate Projections: Seasonal Rainfall over the Hawaiian Islands, *J. Climate*, **22**, 4261–4280, doi: 10.1175/2009JCLI2833.1

(an updated manuscript is in preparation)