Improved Bias Corrected and Downscaled Regional Climate Model Data for Climate Impact Studies: Validation and Assessment for New Zealand

Abstract

Climate impact studies generally require high-resolution, reliable climate data derived from climate model projections. But inherent errors in representing local surface conditions, atmospheric processes and external forcing in Regional Climate Models (RCMs) can lead to considerable systematic biases. Reducing biases in RCM data will lead to more confidence in regional climate impact studies. In this New Zealand case study, the daily temperature and precipitation data from reanalysis forced RCM runs are compared with observed gridded observations. The biases determined for the training period (TRNG, 1980--1999) are used to correct daily data both for the TRNG and a longer but not independent validation period (VLDP, 1972--2000). The biases are computed and corrected using the standard Empirical Quantile Matching (EQM) technique and a newly devised Linked empirical Modelled and Observed Distribution (LeMOD) correction method. Unlike EQM method, the LeMOD bias-correction procedure is designed to remain valid even under nonstationary climatic conditions, though large-scale circulation biases inherent in the driving fields remain. Simple procedures are also proposed to downscale regional climate simulations to higher (0.05 deg) resolution required by many climate impact models. The LeMOD bias corrected daily precipitation is evaluated on the RCM (0.27 deg) and high-resolution grids against VCSN data and is shown to exhibit lower root-mean-square-error and higher temporal correlations than the uncorrected or EQM bias-corrected precipitation. Since reducing model biases decreases the spread in model results in the past climate, this feature is expected to persist in transient climate future projections and contribute towards reducing uncertainties in model projections.

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Improved Bias Corrected and Downscaled Regional Climate1
Model Data for Climate Impact Studies: Validation and2
Assessment for New Zealand3
Abha Sood ∗NIWA, Greta Point, Wellington, New Zealand.4
∗Corresponding author address: Abha Sood, National Institute of Water and Atmospheric Research
(NIWA), 301 Evan Bay Parade, Greta Point, Wellington, 6021, New Zealand.
E-mail: abha.sood@niwa.co.nz
1

ABSTRACT5
Climate impact studies generally require high-resolution, reliable climate data derived6
from climate model projections. But inherent errors in representing local surface conditions,7
atmospheric processes and external forcing in Regional Climate Models (RCMs) can lead to8
considerable systematic biases. Reducing biases in RCM data will lead to more confidence9
in regional climate impact studies. In this New Zealand case study, the daily temperature10
and precipitation data from reanalysis forced RCM runs are compared with observed grid-11
ded observations. The biases determined for the training period (TRNG, 1980–1999) are12
used to correct daily data both for the TRNG and a longer but not independent valida-13
tion period (VLDP, 1972–2000). The biases are computed and corrected using the standard14
Empirical Quantile Matching (EQM) technique and a newly devised Linked empirical Mod-15
elled and Observed Distribution (LeMOD) correction method. Unlike EQM method, the16
LeMOD bias-correction procedure is designed to remain valid even under nonstationary cli-17
matic conditions, though large-scale circulation biases inherent in the driving fields remain.18
Simple procedures are also proposed to downscale regional climate simulations to higher19
(∼0.05◦) resolution required by many climate impact models. The LeMOD bias corrected20
daily precipitation is evaluated on the RCM (0.27◦) and high-resolution grids against VCSN21
data and is shown to exhibit lower root-mean-square-error and higher temporal correlations22
than the uncorrected or EQM bias-corrected precipitation. Since reducing model biases de-23
creases the spread in model results in the past climate, this feature is expected to persist in24
transient climate future projections and contribute towards reducing uncertainties in model25
projections.26
1

1. Introduction27
Regional Climate Models (RCMs) are increasingly becoming an indispensable tool to28
inform a multitude of climate policy relevant issues of major concern to various portfolios such29
as infrastructure, agriculture, water management and renewable energy generation. State-30
of-the-art coupled climate or Atmosphere-Ocean General Circulation Models (AOGCMs)31
capture the general climate reasonably well, though not on a regional scale, lacking the ability32
to simulate accurate regional climatic conditions required to address long term policy issues33
realistically. By resolving spatial features to finer scales, RCM simulations display a much34
improved representation of the spatiotemporal distribution of all the relevant meteorological35
variables. Particularly, simulations of surface temperature and precipitation and of weather36
extremes are much improved compared with their coarser resolution AOGCM counterpart37
(Durman et al. (2001); Christensen et al. (2008); Nikulin et al. (2011)).38
The “added value” in dynamical downscaling lies in the realistic simulation of physically39
consistent spatially resolved fields. The interactions of the large-scale circulation with higher40
resolution orography and other surface features (e.g. land-sea interface, vegetation cover,41
large lakes etc.) are better captured in RCMs, resulting in a diverse range of climatic features42
which are not otherwise resolved. Contrary to some expectations (Racherla et al. (2013);43
Kerr (2013)), reduction of large-scale circulation errors by dynamical downscaling alone is44
not plausible since there are no feedbacks to the larger scales responsible for trends or other45
major climate change signals. Considerable biases in RCM simulations remain (Christensen46
et al. (2008)) even in reanalysis forced simulations where there are negligible circulation errors47
due to assimilation of global observations. This is mostly due to inadequate representation48
of physical processes and external forcing, imperfect lateral and surface boundary conditions49
and limited resolution on the regional scale. Bias-correcting the RCM simulations is a means50
to bridge the wide gap between the data models can provide and the stringent demands on51
climate projection data stipulated by climate impact studies.52
Recently developed statistical bias correction methods vary in complexity; from applying53
2

simple additive correction and scaling factors to more complex methods using regression54
between the well resolved large-scale fields and locally observed climate or matching the dis-55
tributions (Fowler et al. 2007; Ines and Hansen 2006; Teutschbein and Seibert 2012; Maraun56
et al. 2010). Statistical downscaling models simulate weather data at selected locations using57
reliable large-scale atmospheric circulation data on coarse AOGCM or RCM resolution grids58
as predictors for each field individually (Fowler et al. 2007; Watanabe et al. 2012). Unlike59
statistical approach, maintaining spatial and temporal coherence in and between downscaled60
variables is ensured in dynamically downscaled RCM data. Statistical downscaling methods61
are mostly applied on a monthly time scale (Fowler et al. 2007; Li et al. 2010; Ashfaq et al.62
2010) followed by temporal disaggregation when required, and less frequently directly on a63
daily time scale (Baigorria et al. 2007; Piani et al. 2009; Themeßl et al. 2010).64
Most methods also assume that the statistical relationships derived for the past period65
remain stationary. Recently some new procedures to quantify and account for nonstationar-66
ity of climate state were proposed (Maraun 2012; Teutschbein and Seibert 2012; Hertig and67
Jacobeit 2013), where changes in statistical relationships due to changes underlying climate68
states and model ensembles are considered.69
The “Empirical Quantile Matching” (EQM) method is based on a pointwise map from70
simulated to observed cumulative probability distribution function (CDF) of the past cli-71
mate. Here the distribution correction is not derived for concurrent observed and simulated72
variables but by matching quantiles of the two probability distributions. The EQM correc-73
tion is applied to correct quantiles of the past climate and thus used for realistic past climate74
reconstructions by closely matching observations. This correction is applied as an offset to75
the future climate distribution to remove relative biases computed for the past climate.76
In the EQM procedure, the daily model error information directly related to deficiencies77
in representing the underlying processes, which remains invariant under changing climate78
under similar meteorological conditions, is not retained. Moreover in high resolution hydro-79
logical models, stream flow depends strongly on the spatial distribution of precipitation in a80
3

watershed (Maraun 2013) which is not adequately captured by EQM method. An alternative81
method developed in this study is based directly on daily model errors or biases in reanalysis82
driven modelled daily time series projected on the model grid. The modelled and observed83
circulation patterns and synoptic conditions are concurrent for reanalysis forced RCM sim-84
ulations. The model error relationships derived under similar meteorological conditions are85
independent of the past climate statistics. When novel future climate conditions not rep-86
resented in the TRNG period occur, extrapolation is applied to estimate the temperature87
extremes. The precipitation correction is generally more intricate because of its intermittent88
nature and strongly skewed non-normal distribution. Since precipitation extremes are not89
well represented at the multidecadal time scale due to a sparsely populated tail of the distri-90
bution, they are excluded from correction where extrapolation is necessary. The reliability of91
this method is ensured if most weather pattterns are adequately represented in the training92
period and thus the model error distribution is realistic. Though short range extrapola-93
tion beyond observed conditions is valid, for extremes lying far from observed regime, this94
correction strategy may result in large biases and may not be applied.95
Since New Zealand is regionally compact, the computationally formidable task of com-96
piling an ensemble of regional centennial scale climate simulations remains tractable. The97
salient features of the spatial distribution of New Zealand’s climate are governed by its lo-98
cation in the midlatitude southern hemisphere and the interaction of westerly wind with99
the complex steep orography (Sturman and Tapper 2006). This region, subject to strong100
climate variability and encompassing diverse climate zones, is well suited to serve as a test101
bed to examine the impact of bias correction of regional climate change projections. The102
bias correction methods developed in this study are thus simultaneously tested for a diverse103
range of climatic conditions prevalent over New Zealand.104
The main focus of this study is to develop consistent methods to assess and remove biases105
in climate model derived precipitation and surface temperature data. The observed gridded106
data and regional climate model setup used in this study are described in the Sections 2 and107
4

3 respectively. In Sections 4 a and 4 b, the bias correction and downscaling methods are108
described, followed by validation of the bias corrected temperature and precipitation data109
of the past climate in Section 5 and a brief discussion in Section 6.110
2. Gridded Observations111
The observed gridded data set for the New Zealand land surface is compiled at National112
Institute of Water and Atmospheric Research (NIWA) on a regular 0.05◦(or ∼5 km)113
grid from spatially inhomogeneous and temporally discontinuoous quality controlled weather114
station data. The daily estimates of rainfall, potential evapotranspiration, air and vapour115
pressure, maximum and minimum air temperature, soil temperature, relative humidity, solar116
radiation, wind speed and soil moisture at the land surface grid points are referred to as117
“Virtual Climate Station Network” (VCSN) data. These estimates are based on spatial118
interpolation of observations made at weather stations located across New Zealand using a119
“second order derivative trivariate thin plate smoothing spline spatial interpolation model”120
(Tait et al. 2006). The thin-plate smoothing spline model used for the spatial interpolations121
incorporates two location variables (latitude and longitude) and climate pattern for rainfall122
or elevation and lapse rate for temperature (Tait et al. 2006; Tait 2008; Tait et al. 2012). The123
rainfall data records begin in 1960, the wind speed data begin in 1997, and all other time124
series begin in 1972. The time series data are stored in NIWA’s national climate database125
(CLIDB) and can be accessed via a NIWA web portal (CliFlo (2013)).126
The VCSN data for the historic training (TRNG; 1980–1999) and late 20th century127
validation period (VLDP; 1972–2000) are used both for computing biases and validating.128
The gridded VCSN daily maximum temperature (Tmax), minimum temperature (Tmin) and129
accumulated precipitation (P I) fields are extracted for both the TRNG and the VLDP130
hindcast periods. Tmax and Tmin are analysed separately to avoid cancellation of biases and131
masking of errors in the mean daily temperature field (Ackerley et al. 2012). To compute132
5

biases on the same locations, the VCSN gridded data and orography (Fig. 1) were area133
average interpolated from the 0.05◦VCSN resolution to the 0.27◦RCM resolution. The134
daily model biases from the TRNG period are used to correct biases in RCM simulations135
for both periods. The bias-corrected datasets are then validated with the VCSN gridded136
observation data.137
Proper assessment of errors is ensured by using the same topographical data sets in138
the models and gridded observations. Other errors due to interpolation techniques used to139
compile the VCSN data or inherent in archived station observations remain. One example140
where problems may arise is in the mountain valleys, where winter temperature inversions can141
alter the relationship between temperature and elevation and using a constant atmospheric142
lapse rate may not be valid (Tait 2008). Nevertheless, by interpolating observed data on143
the model grid and orography, a fairer comparison of observed data with the model data is144
realized.145
3. RCM description and experiments146
The lateral boundary conditions for the RCM experiments are derived either directly147
from reanalysis data or from global model simulations with the HadAM3p model developed148
by the Hadley Centre, UK. The HadAM3p is a slightly improved version of the atmospheric149
component (AGCM) of HadCM3 with 19 vertical levels and a horizontal grid resolution of150
1.875◦in zonal and 1.25◦meridional directions. HadAM3/HadAM3p have representations151
of all climate relevant fundamenatal atmospheric and land surface processes (Pope et al.152
2000). The parameterized processes in HadAM3p include clouds, radiation, a boundary153
layer scheme, diffusion, gravity wave drag, advection, precipitation and the sulfur cycle. For154
more model details refer to for example, Gordon et al. (2000), Pope and Stratton (2002),155
Pope et al. (2000) and Gregory et al. (1994).156
The Hadley Centre regional climate model HadRM3–PRECIS (Jones et al. 2004) is a157
6

limited area higher-resolution version of HadAM3p using the same parametrization schemes.158
More details of the parametrization of HadRM3 simulations over New Zealand are given in159
Ackerley et al. (2012). The RCM development for the New Zealand region is described in160
previous studies (Bhaskaran et al. 1999, 2002; Drost et al. 2007).161
The RCM domain stretches from around 32◦S–52◦S and 160◦E–193◦E on a regular rotated162
grid with a horizontal resolution of 0.27◦and North pole at 48◦N and 176◦E. By using a163
rotated grid with the equator over the New Zealand domain, quasi-uniform grid box spacing164
is obtained throughout the computational domain. The RCM orography of North, South and165
Stewart Islands in the rotated and the unrotated frame are shown in Fig. 1 (left and middle166
respectively). The small domain of 75×75 grid points, selected to reduce computational time167
for long transient simulations, was shown to be adequate in a previous study (Drost et al.168
2007). A computational time step of 3 minutes is required due to the high spatial resolution.169
The model orography and vegetation data sets were updated from the ones used earlier170
(Drost et al. 2007) to the high resolution surface orography dataset used in the operational171
forecast model at NIWA (Ackerley et al. 2012). There is little difference in the vegetation172
fields. Quasi-equilibrium conditions of the land surface and the overlying atmosphere is173
achieved by allowing a spin up period of one year which is excluded from the analysis.174
The RCM lateral boundary conditions are provided by a) reanalysis data for hindcasts175
and b) HadAM3p (AGCM) forced by CMIP3 sea surface temperatures (SSTs) at the air-sea176
interface for past and future climate simulations.177
a. ERA-40 reanalysis forced simulation178
The RCM is forced at its lateral boundaries by “European Centre for Medium Range179
Weather Forecasts Re-Analysis” (ERA-40) data (Uppala 2005), referred to as REAN, to de-180
liver best estimate of the past weather conditions over New Zealand. The REAN simulation181
is performed to determine the grid cell RCM biases (as in Ackerley et al. (2012)), where182
“perfect” boundary forcings were taken from the ERA-40 reanalysis of the European Centre183
7

for Medium Range Weather Forecasts, so that the errors in large-scale circulation patterns184
compared with observations remain small. The RCM chemistry scheme and the sulfur cycle185
are switched off as atmospheric chemistry data is not available at the lateral boundaries.186
Values for the domain SSTs were interpolated from the HadISST1.1 gridded observations187
data set (Rayner et al. 2003). This simulation used Gregorian calendar (including leap years)188
for the historic reconstruction. The RCM downscaling errors are calculated by comparing189
the reanalysis-forced RCM time series with the VCSN observations over the TRNG period.190
b. CMIP3 SST–AGCM forced simulations191
The Coupled Model Intercomparison Project 3 (CMIP3) data archive compiled for the192
fourth assessment report (AR4) of the “Intergovernmental Panel on Climate Change” (IPCC-193
AR4) (IPCC 2007) comprises of output from AOGCM simulations for the historic period and194
future projections. In the following RCM experiments, from now on referred to as CLIM,195
the “free running” global AGCM - HadAM3p was forced over the ocean by CMIP3 AOGCM196
SSTs and sea ice data taken from selected CMIP3 models to provide lateral boundary condi-197
tions for the RCM simulations. The SST data from CMIP3 simulations were bias corrected198
using HadISST1.1 (Sood et al. 2014) data covering the historical 1961-2000 period. The199
sea-ice concentrations were directly interpolated from the CMIP3 sea-ice dataset. The data200
from CMIP3 20th century experiments with observed external forcings (e.g. greenhouse201
gasses, volacanic emissions (optional), ...) are used to generate the historic climate for each202
CMIP3 model and compared with REAN hindcast simulations. As in the REAN simula-203
tions, the sulfur cycle in the chemistry scheme was not used. The RCM–CLIM simulations204
were performed with 360 days in a model year (12 months of 30 days).205
Both the REAN and CLIM simulations were initialized on 1-December-1969, and run206
until 1-January-2001 and 1-January-2100, respectively. The HadAM3p model time step was207
set to 15 minutes, with 96 time steps per model day. The results shown for only one CMIP3208
member, the HadCM3 model, since all CMIP3 models depict similar behavior though they209
8

may vary in details. All references to the seasons will be DJF (December-January-February),210
MAM (March-April-May), JJA (June-July-August) and SON (September-October-November).211
4. Methods212
In this section the newly developed bias correction and downscaling method for consis-213
tently computing realistic and spatially well resolved RCM data for climate impact applica-214
tions are presented and compared to a popular existing method.215
a. Bias-Correction Methods216
Several different GCM and RCM bias correction and downscaling methods based on217
local rescaling, cumulative probability distribution function (PDF) matching and regression218
techniques have been proposed mainly for monthly and occasionally for daily data (Ines and219
Hansen 2006; Piani et al. 2009; Schmidli et al. 2007; Li et al. 2010).220
In this section, two independent methods to correct observed biases in the past climate221
data are described and applied to the REAN and CLIM precipitation time series. Since222
the temperature correction is simpler and less involved, only the results using the improved223
method LeMOD are presented. Errors after bias correction are compared to errors in the224
uncorrected or control (CTL) data, where the “truth” is taken to be the gridded obser-225
vations (VCSN). The empirical quantile matching (EQM) technique is frequently used for226
bias correcting precipitation data from climate model runs for climate impact studies (Piani227
et al. 2009; Schmidli et al. 2007). The second more elaborate new method presented here is228
based on determining daily biases by comparing REAN and VCSN data for each spatial grid229
point during the TRNG period. Daily model biases are mainly attributed to an inadequate230
representation of local surface conditions impacting land–atmosphere interactions, as well as231
to deficiencies in representing meteorological processes in the RCM simulations. The bias232
corrections are subsequently applied to the past and future CLIM climate projections.233
9

1) Empirical Quantile Matching234
Daily climate time series from dynamically downscaled simulations driven by a “free235
running” climate model can only be compared in a climatological sense with observations236
for the past period (eg. by comparing the statistical properties of their distributions), since237
the weather patterns are not concurrent. A widely used version of a nonparametric EQM238
procedure is applied such that the distributions of the modelled and observed fields for the239
past climate match for each quantile. The adjustment computed for the past climate is240
assumed to be valid for the future climate. This assumption, which may hold for stationary241
climate, is not necessarily be equally valid for a nonstationary climate.242
The daily data are corrected for each month using a 3-month data window from the243
training period centered at the month being processed which does not restrict seasonal244
shifts in future climate.245
The inverse cumulative probability distribution function (or quantiles) of minimum and246
maximum temperature Tm, where m={min, max},of the REAN model (F−1
REAN ,T RNG )247
and observed (F−1
V C SN ,T RNG ) data for the TRNG period are computed. The difference in the248
inverse cumulative probability distribution function of modelled and observed Tmdetermines249
the quantile bias adjustment δTmof the temperature distributions.250
Tcorr
m,CLI M =Tm,CLIM −δTmwhere δTm=F−1
REAN ,T RNG (F(Tm)) −F−1
V C SN ,T RNG (F(Tm)),(1)
The correction term, δTm, determined for the 1980-1999 TRNG period, is applied to the251
REAN and CLIM empirical cumulative probability distribution, FV LDP , over a longer past252
validation period (VLDP) 1972–2000. The correction is applied at each VCSN grid point253
and the bias corrected time series are reconstructed.254
The same procedure is applied to correct biases in precipitation fields. However inter-255
mittent precipitation events result in a strongly skewed precipitation distribution and the256
models tend to simulated too many days of light precipitation. The skew asymmetry in the257
precipitation distribution is much reduced by using truncated wet day data and adjusting258
10

the number of dry days separately. Number of wet days (N–WD) from climate hindcast259
(REAN) data and observations (VCSN) differ considerably. The simulated REAN precipi-260
tation data characterized by more persistent drizzle days substantially overpredict N–WD.261
Similar to previous work by Ines and Hansen (2006), first a precipitation threshold (PT) is262
locally determined at each grid point by matching the number of wet days in the REAN263
and VCSN precipitation data during the TRNG period. Precipitation intensity (PI) in both264
REAN and CLIM data is set to zero below this precipitation intensity threshold, PT. The265
same procedure as described for temperature is then applied to correct the truncated (wet266
days only) precipitation time series at each VCSN grid point and the bias-corrected time267
series are constructed.268
2) Linked empirical Model and Observation Distribution Correction269
The new approach presented here addresses nonstationary effects of transient climate270
change by considering daily biases in the REAN simulations. It is subsequently referred to271
as “Linked empirical Model and Observation Distribution (LeMod)” bias correction method.272
The large-scale circulation errors are avoided in REAN simulations and the observed weather273
sequences are recontructed. The local model biases remaining are solely a result of errors274
in the RCM dynamics, parametrizations of physical processes (e.g. clouds) and the local275
conditions including the representation of unvarying static conditions (e.g. surface height,276
soil characteristics, etc.). Even under nonstationary climatic conditions, predominantly his-277
toric weather conditions are expected to occur, albeit with changes in frequency. The grid278
point model biases derived for conditions of the historic TRNG period remain valid also279
in the future under the same physical conditions represented by the individual bins of the280
PDF. The reliability of this approach is limited by how well the regional climate is repre-281
sented in the arbitrarily selected training period. Bias corrections for the remaining few282
unprecedented extreme climate conditions are derived either by extrapolation (temperature)283
or are left unchanged (precipitation) due to inadequate sparely populated tail of the distri-284
11

bution. The PDF for the future climate is reconstructed by bias correcting data in individual285
bins and by including the frequency change information of historic analogues as well as the286
unprecedented conditions.287
The complex Southern Alps and rugged New Zealand terrain strongly interacts with the288
prevailing westerlies resulting in a myriad of climatic conditions ranging from from subtrop-289
ical to alpine and sub polar and thus constitutes a suitable test bed for evaluating regional290
climate models and bias correction methods. However the sparse and inhomogeneously dis-291
tributed and predominantly low altitude observation station network data may compromise292
the quality of the gridded observation data at high altitudes. Notwithstanding deficiencies in293
modelling orographic precipitation, the added value of regional climate downscaling is most294
apparent in regions lacking robust measurement data over longer time scales.295
The new approach involves computing the model biases by comparing REAN temperature296
data at each grid point, i, in each bin, b, of the PDF with the concurrent observations from297
the VCSN dataset. Only the mapped mean and standard deviation of the VCSN data298
for each bin, b, of the REAN data are retained for the 20-year TRNG period. Seasonal299
probability distributions of surface minimum (Tmin) and maximum (Tmax) temperature at300
each RCM grid point iare compiled. In each temperature distribution bin, b, of width 1◦C,301
the model mean Tb,i and standard deviation σ(Tb,i) are rescaled using the linked observed302
mean, TV CS N
b,i , and standard deviation σTV CS N
b,i for days tb,i in the bin, b, at grid point, i.303
The corrected temperature Tcorr
b,i =Tcorr (tb,i) is computed as follows:304
Tcorr (tb,i) = T(tb,i )−Tb,i·σTV C SN
b,i /σ(Tb,i ) + TV CS N
b,i (2)
To illustrate this method, Fig. 2 shows the modelled DJF maximum temperature data305
(red) for the 20–21◦C bin and the corresponding observed data (black). The mean and306
variance of the observed data are used to shift and rescale the mean and variance of the model307
data (red) to compute the bias corrected values (blue). The bias corrected temperature shows308
a more realistic scatter and has a root mean square (RMS) error 2.68 compared with 3.65309
for the raw data in this example. The RMS error improves most on grid points exhibiting310
12

large biases. Where biases are small, the RMS error is of the same order of magnitude as311
for the raw data. The rescaling standard deviation term in the bias correction procedure312
mostly results in a significant increase in variance to match the observed variance.313
For the precipitation data, the dry days are defined as days where the precipitation314
intensity is below the precipitation threshold (PT) as described in the last section. The315
precipitation intensity is set to zero below PT in the REAN as in the EQM method. The316
intermittent nature of precipitation is considered using a moving average over a multiple317
day window. Since autocorrelation beyond two neighbouring days is low, a running mean318
window of 5 days centred on the day under consideration, t, is selected. This approach319
enhances the correction of multiple-day precipitation events and partially retains short term320
autocorrelation of the observed time series.321
The daily precipitation distributions of the REAN data (bin width: 1 mm/day) for the322
TRNG period and the concurrent 5–day running mean and standard deviation values of the323
REAN and VCSN time series are compiled. The precipitation correction P IREAN
corr,i (t) for each324
day, t, of the time series and each grid point, i, is computed.325
P I REAN
corr,i (t) = P I REAN
i(t)−P I REAN
i(t)5d·σ5dP I V CSN
i(t)
σ5dP I REAN
i(t)+P I V CSN
i(t)5d(3)
For REAN simulations beyond the TRNG period and for future and past climate simual-326
tions, concurrent observed values are not used or not available. Instead for each bin bof327
simulated precipitation distribution, P Ib,i, the minimum euclidean distance Db,i of the model328
mean and standard deviation of the running means time series, to P I REAN
ifor all elements329
in the bin bis determined as follows.330
Db,i(s) = min 


P Ib,i
5d, σ5d(P Ib,i)−P I REAN
b,i
5d, σ5dP I REAN
b,i 


(4)
and the corresponding time point sis determined. Therefore, for the REAN simulation in the331
TRNG period, this value is 0. If no observed values are present in a bin b, then the selection332
is expanded to include adjacent bins until the extremal bin bmax is reached. Similarly, for333
P I CLIM
i(t), the REAN and concurrent VCSN running mean and standard deviation values334
13

at time point, s, determined in eq. 4 are used to correct the precipitation bias.335
P I CLIM
corr,i (t) = P I CLIM
i(t)−P I REAN
i(s)5d·σ5dP I V CSN
i(s)
σ5dP I REAN
i(s)+P I V CSN
i(s)5d(5)
This procedure leads to excessive smoothing in sparsely populated bins so that a signif-336
icant decrease in accuracy and reliability occurs in the tail of the distribution. Therefore337
no correction is applied at the tail of the precipitation distribution beyond a 99.5 percentile338
threshold. Thus the model extremes is obtained using this approach are consistent with339
REAN dataset but not bias corrected.340
b. Downscaling Methods341
For most climate impact impact studies, considerably higher spatial resolution is stipu-342
lated. In the following, simple physicially moviated first order downscaling procedures are343
suggested for the coarse resolution bias corrected temperature and precipitation data. Since344
most climate impact studies require regular lat-lon grid, the bias-corrected RCM data are345
first unrotated at the original resolution (0.27◦).346
1) Temperature347
The data is lapsed on to the sea level at all land grid points using a constant lapse rate348
(5 K/km) (Tait 2008, 2010) and the RCM orography. It is bilinearly interpolated at sea349
level to the high resolution (0.05◦) grid, whereby sea points are masked to avoid negative350
biases. The masking of coarse resolution sea points results in missing data in a few coastal351
land points in the high resolution data set. The data is then lapsed to the land surface using352
a more accurate high-resolution elevation data set and the same lapse rate.353
14

2) Precipitation354
No simple relationship exists for elevation and precipitation analogous to a lapse rate for355
elevation and temperature, but significant corrections to bilinear interpolation downscaling356
are required where strong orographic forcing is present (Engen-Skaugen 2007). Similar to357
the lapse rate based correction for temperature, local corrections based on the difference358
between RCM and VCSN elevation and the wind direction of the zonal wind component at359
700 hPa (|u700|>3m/s) are applied. Orographic precipitation enhancement factor varies360
from 1.5–4.5/1000 m in the literature (Haiden and Pistotnik 2009) based on a regional case361
study in the European Alps.362
In lieu of direct observations in the Southern Alps, an enhancement factor of 0.8/1000 m363
and a reduction factor of 0.5/1000 m was selected by roughly reconstructing the largest364
annual mean value on the VCSN grid and based on VCSN data for the TRNG period.365
These factors are used over all land grid points with no further tuning. This is not a366
rigorous but a pragmatic attempt to reconstruct a plausible, realistic and consistent high367
elevation precipitation data set at climate relevant time scales. The correction term was368
obtained by multipling the enhancement (reduction) factor to elevation difference between369
the binearly interpolated coarse resolution (0.27◦) and the left neighbouring high resolution370
(0.05◦) data. The enhancement (reduction) term was added to the biased corrected and371
bilnearly interpolated RCM precipitation on the same 0.05◦VCSN grid. Thus precipitation372
enhancement occurs on the windward side of the orographic divide, while on the leeward373
side, due to rain shadow effect, there is a reduction in precipitation. At low lying locations374
where the elevation difference remain small, the correction is negligible.375
5. RCM simulations and validation376
The seasonal and annual validation of bias corrected data is presented for the TRNG and377
past late 20th century (VLDP).378
15

a. Model Biases379
The maximum (Tmax) and minimum (Tmin) temperature and precipitation (P I ) biases380
in the REAN simulations with respect to the VCSN data for the TRNG period have been381
discussed previously in considerable detail (Ackerley et al. 2012). The coarse climatic fea-382
tures, for example the spatial distribution and the annual cycle of maximum and minimum383
surface air temperatures, are well captured (Fig. 3, rows 1 and 3). The fine scale spatial384
and temporal comparisons reveal considerable temperature biases, with negative biases in385
maximum temperature and positive biases in minimum temperature, underestimating the386
daily temperature range (not shown). The model captures the west–east gradient in precipi-387
tation across the Southern Alps well (Fig. 4, row 1) but with large negative or positive biases388
in most regions (Fig. 4, rows 2 and 3). Biases in the CLIM results have a similar spatial389
pattern but are larger in magnitude than those in the reanalysis-forced run due to additional390
circulation errors. The circulation errors are attributed to biases in the SST forcing and the391
AGCM simulations as well as to internal variability of the climate system.392
b. Training period validation393
Model errors for the daily time series are determined for the training period. The LeMOD394
bias corrected REAN surface temperature and precipitation data are compared with VCSN395
data (Fig. 3 and 4). The remaining bias in the LeMOD bias-corrected minimum and396
maximum temperature data remain below 0.5◦C at all grid points. The diurnal temperature397
range is considerably improved as a result of the large reduction in biases in both minimum398
and maximum temperature.399
The mean seasonal and annual precipitation exhibits mostly wet bias along the orographic400
features along the windward slopes whereas most of the other regions experience a dry bias401
(Fig. 4). There is a maximum bias of up to 20% remaining after bias correction (row 4)402
in most regions. Larger biases remain over central North Island and south eastern South403
16

Island, which is a reflection of large biases present in the RCM (CTL) data.404
c. Past climate validation405
In this section, biases in minimum and maximum 1.5m temperature and precipitation406
data from the REAN simulations with respect to concurrent VCSN gridded observations407
determined earlier for the TRNG period are applied to data over a longer past VLDP period.408
For this study, only a short 29 year period of simultaneous REAN and VCSN data are409
available. Therefore validation based on longer period excluding the TRNG period was not410
possible. Validation for considerably shorter periods of under 10 year though possible are411
expected to exhibit larger biases.412
As in the TRNG period, the mean seasonal bias corrected minimum and maximum413
temperature are substantially improved for the VLDP period with mostly a small cool bias414
below 0.5◦C in magnitude (Fig. 5) except in limited regions for maximum temperature415
where there is a cool bias of up to 1.0◦C in magnitude (Fig. 5, row 4).416
The mean seasonal and annual LeMOD precipitation exhibits substantially lower biases417
compared with CTL precipitation for the VLDP period which includes the TRNG period.418
The magnitude of biases in LeMOD precipitation (Fig. 6, row 3) is mostly the same as for419
the TRNG period (Fig. 4, row 3). All seasons are marginally drier with autumn (MAM) and420
winter (JJA) seasons depicting the largest differences. The magnitude of EQM precipitation421
biases is larger than for LeMOD precipitation in all seasons as well as annually (Fig. 6, rows422
3 and 4).423
d. Comparison of Bias Correction Methods424
The assessment of bias correction methods for precipitation is based on the correlation425
coefficient and root mean square error with the observed VCSN data of the past validation426
period (VLDP). Since the surface temperature fields have lower uncertainty and the biases427
17

are simpler to correct, they are not assessed further. The correlation coefficient for the428
LeMOD precipitation time series (Fig. 7, right) is considerably higher on all grid point than429
for the CTL (Fig. 7, left) or EQM (Fig. 7, middle) precipitation. The root mean square430
error is considerably lower for LeMOD bias corrected time series (Fig. 8, right) than for the431
CTL (Fig. 8, left) or EQM bias corrected (Fig. 8, middle) data. As seen in Fig. 7 and Fig. 8432
(middle), there is only limited improvement of the correlation coefficient or root mean square433
error of EQM bias corrected data compared with the uncorrected CTL data.434
The corresponding downscaled precipitation at 0.05◦grid size broadly exhibits the same435
charcteristics as on the model resolution of 0.27◦for the VLDP period. A substantial increase436
in correlation coefficient is observed for the LeMOD precipitation at all land grid points437
whereas not much difference is observed between the EQM and CTL precipitation (Fig. 9).438
The root mean square error is again lower for the LeMOD precipitation indicated by blue439
shades in Fig. 10 (right), but some regions (in red) show some increase. The regions showing440
deterioration in RMSE with respect to VCSN data are influenced by prominent orographic441
features where VCSN data accuracy may be lacking. The reduction in root mean square442
error is much less in the EQM precipitation (Fig. 10, middle) compared with the LeMOD443
precipitation (Fig. 10, right) but broadly depicts the same spatial features.444
e. Validation of climate simulations445
The surface temperature and precipitation climatological data for two ensemble members446
of RCM simulations of the 20th century hindcast for HadCM3 (HadCM3–A2-1 and HadCM3–447
A2-2 referred to as CLIM) from IPCC AR4 are validated for the VLDP period. The mean448
seasonal and annual LeMOD bias corrected minimum temperature is substantially improved449
for the VLDP period with a small cool bias remaining mostly below 0.5◦C in magnitude450
for all seasons (Fig. 11). Also the seasonal and annual maximum temperature biases are451
considerably improved, though the seasonal biases are marginally larger with positive and452
negative fluctuations in different seasons (Fig. 12). The minimum and maximum temperature453
18

biases in both simulations are nearly identical (see rows 3 and 4 in Fig. 11 and Fig. 12).454
The mean seasonal and annual bias in the LeMOD precipitation for the HadCM3–A2-1455
and HadCM3–A2-2 simulations in the VLDP period have a similar pattern as the LeMOD456
precipitation from REAN run but with mostly up to 20% larger wet bias (Fig. 13). The larger457
biases are caused by deviations in the large-scale circulations and are expected partly due to458
internal variability of the climate system in absence of data assimilation, model errors and459
inherent climate uncertainty. Such enhanced biases in the temperature field are not observed460
since surface temperature is influenced by large-scale circulation to a lesser degree.461
The regional differences in mean seasonal spatial distribution of LeMOD precipitation462
(Fig. 13) and EQM precipitation (Fig. 14) in HadCM3–A2-1 and HadCM3–A2-2 simulations463
in VLDP period are small with slightly wetter conditions in the spring and summer seasons464
and drier conditions in autumn and winter in LeMOD vs. EQM precipitation.465
6. Discussion and Conclusions466
Bias correction of regional climate data is indispensable for most climate impact studies.467
The main challenge in this study is to correct data on a daily time scale using a more468
rigorous approach in an attempt to provide realistic information regarding the higher modes469
of variability of “weather within climate” (Ines and Hansen 2006). For realistic and reliable470
output, it is also necessary to validate and assess the bias correction methods. Since model471
errors are largest in precipitation simulations, and this is a crucial field for almost all climate472
impact investigations, detailed validation and evaluation for two bias correction methods,473
EQM and LeMOD, are performed. Surface temperature is less influenced by uncertainties474
in large-scale circulation fields than precipitation and the systematic biases are mostly due475
to inadequate representation of local conditions such as orography and aspect, hence these476
data are considerably less problematic to correct.477
The LeMOD technique uses a semi-empirical statistical approach to correct errors in478
19

the frequency distribution of model data. It is a new approach to correct biases in RCM479
simulations using deviations between REAN climate hindcast data and gridded observations480
on a daily time scale. Biases in meteorological variables occur due to model errors and the481
description of local conditions since large-scale circulation errors in simulations forced by482
reanalysis data at the lateral boundaries are strongly supressed. Even though the distribution483
changes with time under nonstationary climatic conditions, most of the weather states that484
occur will be similar to the ones in the past with the same error distribution and statistics. A485
sufficiently long 20–year model hindcast and observation period ensures adequate sampling486
of the model errors. If a representative training period is used to sample model errors,487
the biases under the same conditions remain unchanged. This will be valid even in the488
case of nonstationary climate change where the distribution changes. This feature is unlike489
other methods (Maraun 2012; Ines and Hansen 2006; Li et al. 2010) based on statistical490
relationships between large-scale predictors and regional or local scale predictands derived491
for the past period, or distribution-matching techniques, which remain valid for the future492
period only for a quasi-stationary climate.493
However the mapping of similar meteorological conditions in this study is only based on494
the same PDF bins. Attempt for define conditions on large scale meteorological conditions495
were sofar not successful. More work is require to improve the mapping to similar meteorog-496
ical conditions resulting in better implementation of a bias correction approach empirically497
based on model errors.498
A limited number of novel unprecedented weather conditions not occuring during the499
TRNG period will mostly be located in the tail of the distribution. Since the temperature500
distribution is smooth, a simple approach to use the values in the tail of the distribution501
corrected the values neighbouring bins provide a good estimate. However the tail of the502
precipitation distribution is very sparsely populated. Hence the precipitation extremes above503
a prescibed critical 99.5 percentile threshold in the sparsely sampled tail are excluded from504
bias correction.505
20

The seasonal and annual REAN and CLIM surface temperature fields in the climate506
hindcast period (VLDP) are considerably improved (see Section 5), while small local biases507
of less than 1K remain. This suggests that the proposed LeMOD bias correction method508
for surface temperature is applicable to bias correct future climate projection data and to509
obtain realistic estimates of the regional surface temperature change signal. The regional510
climate projections forced by different SRES emission scenarios in the early part of the 21st
511
century do not deviate much from the late 20th century historic period. Stronger deviations512
are present in the mid and late 21st century.513
The 5-day running mean REAN-CTL precipitation time series are corrected using the514
corresponding VCSN time series, where the mean and standard deviation of the “observed”515
data in the CTL precipitation distribution [mm/day] bins is used to compute biases. The516
seasonal and annual REAN and CLIM precipitation is significantly improved with relatively517
small biases remaining in the past VLDP period for both LeMOD and EQM bias correction518
methods.519
However comparison of temporal correlations of the two bias-corrected RCM time series520
with VCSN grid point time series reveals considerable differences. The correlation coefficient521
of LeMOD and VCSN precipitation is larger than that of either the CTL or EQM precip-522
itation. The root mean square error of LeMOD daily precipitation is also reduced at all523
grid points confirming a better temporal match. This is the expected result since the EQM524
method does not use the temporal information but equates quantiles of CTL and VCSN525
precipitation whereas LeMOD preserves an imprint of temporal structure of the CTL and526
VCSN precipitation mapped on the daily time scale. A simple mapping of derived REAN527
precipitation (see equation 4) and observed precipitation for the VLDP period is a simple528
but an effective procedure.529
Some improvement of the downscaling procedure (Section 4 b) is feasible by using eight530
wind sectors instead of only the two dominant east–west directions in regions influenced531
by other prevailing wind directions. Note that more complex interactions of large-scale532
21

atmospheric variables and local complex terrain, for example in deep valleys, are not captured533
by the interpolation methods.534
Recent investigations (Maraun 2013) suggested that correcting and downscaling to point535
scale (observation station) using standard deviation adjustment or quantile matching tech-536
nique leads to larger temporal errors. An alternative procedure suggested in this study is537
to bias correct data on the model grid scale and use additional information to downscale to538
the local or point scale using simple physical or statistical relationships. LeMOD performs539
better than arguably so far the best performing QM technique (Themeßl et al. 2010).540
The LeMOD bias correction and interpolation based downscaling procedure provides541
improved high-resolution climate change estimates of temperature and precipitation and is542
very promising for climate impact applications. It is expected that reducing model biases543
will result in reducing the spread of transient climate response to the external forcing, thus544
increasing confidence in future climate projections through removal of a significant propor-545
tion of regional modelling errors. The implications of bias correction of transient climate546
responses and its application to climate impacts on primary sectors of the economy including547
agriculture, renewable energy generation and water resource management will be discussed548
in a future study.549
Acknowledgments.550
This work was supported by New Zealands core research Regional Modelling of Future551
New Zealand Climate. I will like to take this opportunity to thank Andrew Tait for providing552
the VCSN data and Lara Wilcocks for providing scripts to extract data from NIWA archive.553
I also thank Brett Mullan, Sam Dean and Stephen Stuart for numerous discussions and554
Duncan Ackerley and Stephen Stuart for running climate simulations on NIWA’s HPCF.555
This work has been submitted for publication. Copyright in this work may be transferred556
without further notice, and this version may no longer be accessible.557
22

558
REFERENCES559
Ackerley, D., S. Dean, A. Sood, and A. B. Mullan, 2012: Regional climate modeling in NZ:560
Comparison to gridded and satellte observations. Wea. Clim.,32 (1), 3–22.561
Ashfaq, M., L. C. Bowling, K. Cherkauer, J. S. Pal, and N. S. Diffenbaugh, 2010: Influence of562
climate model biases and dailyscale temperature and precipitation events on hydrological563
impacts assessment: A case study of the united states. Journal of Geophysical Research,564
115, 1–15, doi:10.1029/2009JD012965.565
Baigorria, G. A., J. W. Jones, D.-W. Shin, A. Mishra, and J. J. O’Brien, 2007: Assessing un-566
certainties in crop model simulations using daily bias-corrected regional circulation model567
outputs. Clim. Res.,34, 211–222, doi:10.3354/cr00703.568
Bhaskaran, B., A. B. Mullan, and J. Renwick, 1999: Modelling of atmospheric variation at569
NIWA. Wea. Clim.,19, 23–36.570
Bhaskaran, B., J. Renwick, and A. B. Mullan, 2002: On application of the Unified Model to571
produce finer scale climate information. Wea. Clim.,22, 19–27.572
Christensen, J. H., F. Boberg, O. B. Christensen, and P. Lucas-Picher, 2008: On the need573
for bias correction of regional climate change projections of temperature and precipitation.574
Geophys. Res. Lett.,35, doi:10.1029/2008GL035694.575
CliFlo, 2013: New Zealand’s National Climate Database. NIWA, http://cliflo.niwa.co.576
nz.577
Drost, F., J. Renwick, B. Bhaskaran, H. Oliver, and J. L. MacGregor, 2007: Simulation of578
New Zealand’s climate using high resolution regional climate model. Intl. J. Climatol.,27,579
1153–1169.580
23

Durman, C. F., J. M. Gregory, D. Hassell, R. G. Jones, and J. M. Murphy, 2001: A compar-581
ison of extreme european daily precipitation simulated by a global and a regional climate582
model for present and future climates. Q. J. R. Meteorol. Soc.,127, 1005–1015.583
Engen-Skaugen, T., 2007: Refinement of dynamically downscaled precipitation and temper-584
ature scenarios. Climatic Change,84, 365–382, doi:10.1007/s10584-007-9251-6.585
Fowler, H. J., S. Blenkinsop, and C. Tebaldi, 2007: Linking climate change modelling to586
impacts studies: recent advances in downscaling techniques for hydrological modelling.587
Intl. J. Climatol.,27, 1547–1578, doi:10.1002/joc.588
Gordon, C., C. Cooper, C. A. Senior, H. Banks, J. M. Gregory, T. C. Johns, J. F. B. Mitchell,589
and R. A. Woods, 2000: The simulation of SST, sea ice extents and ocean heat transports590
in a verion of Hadley Centre coupled model without flux adjustments. Clim. Dyn.,16,591
147–168.592
Gregory, D., R. N. B. Smith, and P. M. Cox, 1994: Canopy, surface and soil hydrology,593
version 3. Unified model documentation, UK Met Office. Also available as http://cms.594
ncaas.ac.uk/html\_umdocs/vn4.5/p025.pdf.595
Haiden, T. and G. Pistotnik, 2009: Intensity-dependent parameterization of elevation effects596
in precipitation analysis. Adv. Geosci.,20, 33–38.597
Hertig, E. and J. Jacobeit, 2013: A novel approach to statistical downscaling considering598
nonstationarities: application to daily precipitation in the mediterranean area. Journal of599
Geophysical Research,118, 1–14, doi:10.1002/jgrd.50112.600
Ines, A. V. M. and J. W. Hansen, 2006: Bias correction of daily gcm rainfall for crop601
simulation studies. Agric. Forest Meteorol.,138, 44–53.602
IPCC, 2007: Contribution of Working Group I to the Fourth Assessment Report of the603
24

Intergovernmental Panel on Climate Change. Climate Change 2007: The Physical Science604
Basis, Cambridge University Press.605
Jones, R., M. Noguer, D. C. Hassell, D. Hudson, S. S. Wilson, G. J. Jenkins, and J. F. B.606
Mitchell, 2004: Generating high resolution climate change scenarios using PRECIS. Tech.607
rep., Met Office Hadley Centre, UK, 40 pp.608
Kerr, R. A., 2013: Forecasting regional climate change flunks its first test. Science,339,609
638–638, doi:10.1126/science.339.6120.638.610
Li, H., J. Sheffield, and E. F. Wood, 2010: Bias correction of monthly precipitation and tem-611
perature fields from intergovernmental panel on climate change ar4 models using equidis-612
tant quantile matching. J. Geophys. Res.,115, doi:10.1029/2009JD012882.613
Maraun, D., 2012: Nonstationarities of regional climate model biases in european seasonal614
mean temperature and precipitation sums. Geophys. Res. Lett.,39 (L06706), 1–5, doi:615
10.1029/2012GL051210.616
Maraun, D., 2013: Bias correction, quantile mapping and downscaling: revisiting the infla-617
tion issue. J. Clim.,26, 2137–2143, doi:10.1175/JCLI-D-12-00821.1.618
Maraun, D., et al., 2010: Precipitation downscaling under climate change: Recent develop-619
ments to bridge the gap between dynamical models and the end user. Rev. Geophys., 48,620
RG3003, doi:87551209/10/2009RG000314.621
Nikulin, G., E. Kjellstroem, U. Hansson, G. Strandberg, and A. Ullerstig, 2011: Evaluation622
and future projections of temperature, precipitation and wind extremes over europe in623
an ensemble of regional climate simulations. Tellus,63A, 41–55, doi:10.1111/j.1600-0870.624
2010.00466.x.625
Piani, C., J. Haerter, and E. Coppola, 2009: Statistical bias correction for daily pre-626
25

cipitation in regional climate models over europe. Theo. App. Climatol., doi:10.1007/627
s00704-009-0134-9.628
Pope, V. D., M. L. Gallani, and P. R. Rowntree, 2000: The impact of new physical629
parametrization in the hadley centre climate model: Hadam3. Clim. Dyn.,16, 123–146.630
Pope, V. D. and R. A. Stratton, 2002: The process governing horizontal resolution sensitivity631
in a climate model. Clim. Dyn.,19, 211–236, doi:10.1007/s00382-001-0222-8.632
Racherla, P. N., D. T. Shindell, and G. S. Faluvegi, 2013: The added value to global model633
projections of climate change by dynamical downscaling: A case study over the continental634
u.s. using the giss-modele2 and wrf models. J. Geophys. Res.,117, D20118, doi:10.1029/635
2012JD01809.636
Rayner, N. A., D. E. Parker, E. B. Horton, C. K. Folland, L. V. Alexander, D. P. Rowell,637
E. C. Kent, and A. Kaplan, 2003: Global analysis of sea surface tempertaure, sea ice and638
night marine air tempreature since the nineteenth cetury. J. Geophys. Res.,108 (D14),639
doi:10.1029/2002JD002670.640
Schmidli, J., C. M. Goodess, C. Frei, M. R. Haylock, Y. Hundecha, J. Ribalaygua, and641
T. Schmith, 2007: Statistical and dynamical downscaling of precipitation: An evaluation642
and comparison of scenarios for the european alps. J. Geophys. Res.,112, 101 029, doi:643
10.1029/2005JD007026.644
Sood, A., S. Stuart, and B. Mullan, 2014: Variability of climate change signal over New645
Zealand in 21st century CMIP3 transient regional climate model simulations. In prepa-646
ration.647
Sturman, A. and N. J. Tapper, 2006: The weather and climate of Australia and New Zealand.648
Oxford University Press, Melbourne, 541 pp.649
26

Tait, A., R. Henderson, R. Turner, and X. Zheng, 2006: Thin plate smoothing spline inter-650
polation of daily rainfall for New Zealand using climatological rainfall surface. Intl. J. Cli-651
matol.,26, 2097–2115.652
Tait, A., J. Sturman, and M. Clark, 2012: An assessment of the accuracy of interpolated653
daily rainfall for New Zealand. J. Hydrol.(NZ),51 (1), 25–44.654
Tait, A. B., 2008: Future projections of growing degree days and frost in New Zealand and655
some implications for grape growing. Wea. Clim.,28, 17–36.656
Tait, A. B., 2010: Comparison of two interpolation methods for daily maximum and mini-657
mum temperatures for new zealand. stage 3: Comparison with independent high elevation658
temperature data, internal document.659
Teutschbein, C. and J. Seibert, 2012: Is bias correction of regional climate model (rcm)660
simulations possible for non-stationary conditions? Hydrol. Earth Syst. Sci. Discuss.,9,661
12 765–12 795, doi:10.5194/hessd- 9-12765-2012.662
Themeßl, M. J., A. Gobiet, and A. Leuprecht, 2010: Empirical-statistical downscaling and663
error correction of daily precipitation from regional climate models. Intl. J. Climatol.,664
doi:10.1002/joc.2168.665
Uppala, S. M. e. a., 2005: The ERA-40 re-analysis. Q.J.R. Meteorol. Soc.,131 (612),666
2961–3012, doi:10.1256/qj.04.176, URL http://dx.doi.org/10.1256/qj.04.176.667
Watanabe, S., S. Kanae, S. Seto, P. J.-F. Yeh, Y. Hirabayashi, and T. Oki, 2012: Inter-668
comparison of bias-correction methods for monthly temperature and precipitation sim-669
ulated by multiple climate models. Journal of Geophysical Research,117, 1–13, doi:670
10.1029/2012JD018192.671
27

List of Figures672
1 Orography [in m a.s.l.] on 0.27◦RCM grid in rotated (left; rotated north pole673
at 48◦N, 176◦E) frame, unrotated frame (middle) and on the standard 0.05◦
674
VCSN grid in unrotated frame (right). 30675
2 Maximum DJF temperature (raw, red) for grid cell ifrom REAN simulation in676
the temperature range of 20–21◦C over the VLDP time period, the concurrent677
observed data (black) and the bias corrected temperature (blue) is presented678
in the upper panel. The lower panel shows differences in the CTL and bias679
corrected temperature data to the VCSN data taken from the upper panel. 31680
3 Mean seasonal and annual bias-corrected (LeMOD) minimum temperature,681
Tmin [◦C] (row 1) and remaining bias (2.row), bias corrected maximum tem-682
perature, Tmax [◦C] (row 3) and remaining bias (row 4) from REAN simu-683
lations in the 1980–1999 training (TRNG) period are presented on rotated684
coordinate RCM grid (North pole: 48N, 176E). 32685
4 Mean seasonal and annual bias corrected (LeMOD) REAN precipitation P I686
in [mm/day], bias in [mm/day] and [%] for the TRNG period and bias after687
correction in [%] are depicted in rows 1 to 4 respectively. 33688
5 Same as Fig. 3 except for past validation period (VLDP, 1972–2000). 34689
6 Mean seasonal and annual bias corrected (LeMOD) daily REAN precipitation690
P I in [mm/day], bias in CTL, bias after LeMOD correction and bias after691
EQM correction [%] for the past validation period (VLDP, 1972–2000) are692
presented in rows 1–4 respectively. 35693
7 Linear correlation coefficient of CTL (left), EQM (middle) and LeMOD (right)694
bias corrected daily precipitation time series with respect to VCSN gridded695
observations 36696
28

8 Root Mean Square Error (RMSE) of CTL (left) daily precipitation in [mm/day],697
and reduction in RMSE [%] of EQM (middle) and LeMOD (right) bias cor-698
rected daily precipitation with respect to CTL data (left). 37699
9 Same as Fig. 7 except on 0.05◦resolution 38700
10 Same as Fig. 8 except on 0.05◦resolution. 39701
11 Mean seasonal and annual bias corrected minimum temperature (Tmin) for702
HadCM3–A2-1 simulation [◦C] (row 1), the bias before (row 2) and after703
(row 3) LeMOD correction for HadCM3–A2-1 and the bias after correction704
(4.row) for HadCM3–A2-2 simulation are presented for the past validation705
period (VLDP, 1972–2000). 40706
12 Same as Fig. 11 except for maximum temperature (Tmax ). 41707
13 Same as in Fig. 11 except for precipitation intensity [mm/day] (PI). 42708
14 Bias corrected (EQM) daily REAN precipitation P I in [mm/day] (rows 1 and709
2) and bias after correction (rows 3 and 4) in [%] in CLIM HadCM3–A1 and710
HadCM3–A2-2 simulations for the past VLDP validation period. 43711
29

Fig. 1. Orography [in m a.s.l.] on 0.27◦RCM grid in rotated (left; rotated north pole
at 48◦N, 176◦E) frame, unrotated frame (middle) and on the standard 0.05◦VCSN grid in
unrotated frame (right).
30

TM ax[◦C]TM ax[◦C]
Fig. 2. Maximum DJF temperature (raw, red) for grid cell ifrom REAN simulation in the
temperature range of 20–21◦C over the VLDP time period, the concurrent observed data
(black) and the bias corrected temperature (blue) is presented in the upper panel. The lower
panel shows differences in the CTL and bias corrected temperature data to the VCSN data
taken from the upper panel.
31

DJF MAM JJA SON ANN
TBC
min
bias(TBC
min)TBC
max
bias(TBC
max)
Fig. 3. Mean seasonal and annual bias-corrected (LeMOD) minimum temperature, Tmin
[◦C] (row 1) and remaining bias (2.row), bias corrected maximum temperature, Tmax [◦C]
(row 3) and remaining bias (row 4) from REAN simulations in the 1980–1999 training
(TRNG) period are presented on rotated coordinate RCM grid (North pole: 48N, 176E).
32

DJF MAM JJA SON ANN
P IBC [mm/day]bias(P recCT L )[mm/day]bias(P recC T L)[%]bias(P recB C )[%]
Fig. 4. Mean seasonal and annual bias corrected (LeMOD) REAN precipitation P I in
[mm/day], bias in [mm/day] and [%] for the TRNG period and bias after correction in [%]
are depicted in rows 1 to 4 respectively.
33

DJF MAM JJA SON
ANN
TBC
min
bias(TBC
min)TBC
max
bias(TBC
max)
Fig. 5. Same as Fig. 3 except for past validation period (VLDP, 1972–2000).
34

DJF MAM JJA SON ANN
P IBC [mm/day]
CTL bias [%]LeMOD bias [%]EQM bias [%]
Fig. 6. Mean seasonal and annual bias corrected (LeMOD) daily REAN precipitation P I
in [mm/day], bias in CTL, bias after LeMOD correction and bias after EQM correction [%]
for the past validation period (VLDP, 1972–2000) are presented in rows 1–4 respectively.
35

Fig. 7. Linear correlation coefficient of CTL (left), EQM (middle) and LeMOD (right) bias
corrected daily precipitation time series with respect to VCSN gridded observations
36

Fig. 8. Root Mean Square Error (RMSE) of CTL (left) daily precipitation in [mm/day],
and reduction in RMSE [%] of EQM (middle) and LeMOD (right) bias corrected daily
precipitation with respect to CTL data (left).
37

Fig. 9. Same as Fig. 7 except on 0.05◦resolution
38

Fig. 10. Same as Fig. 8 except on 0.05◦resolution.
39

DJF MAM JJA SON ANN
TBC
min (HadCM3-A2-1)
bias (HadCM3-A2-1)
biasBC (HadCM3-A2-1)biasB C (HadCM3-A2-2)
Fig. 11. Mean seasonal and annual bias corrected minimum temperature (Tmin) for
HadCM3–A2-1 simulation [◦C] (row 1), the bias before (row 2) and after (row 3) LeMOD
correction for HadCM3–A2-1 and the bias after correction (4.row) for HadCM3–A2-2 sim-
ulation are presented for the past validation period (VLDP, 1972–2000).
40

DJF MAM JJA SON ANN
TBC
max (HadCM3-A2-1)
bias (HadCM3-A2-1)
biasBC (HadCM3-A2-1)biasBC (HadCM3-A2-2)
Fig. 12. Same as Fig. 11 except for maximum temperature (Tmax).
41

DJF MAM JJA SON ANN
P IBC (HadCM3-A2-1)
bias (HadCM3-A2-1)
biasBC (HadCM3-A2-1)biasBC (HadCM3-A2-2)
Fig. 13. Same as in Fig. 11 except for precipitation intensity [mm/day] (PI).
42

P IBC (HadCM3-A2-1)
bias (HadCM3-A2-1)
bias (HadCM3-A2-1)bias (HadCM3-A2-2)
Fig. 14. Bias corrected (EQM) daily REAN precipitation P I in [mm/day] (rows 1 and 2)
and bias after correction (rows 3 and 4) in [%] in CLIM HadCM3–A1 and HadCM3–A2-2
simulations for the past VLDP validation period.
43