Bias corrected CMIP5 output

Previous studies where GLAM was used have employed raw climate model output directly into the crop model, with only a limited account for climate model bias through the calibration of CY G (Challinor et al., 2007, 2009a, 2010), or have reported little benefit

from bias correction (Challinor et al., 2005a). Nevertheless, climate model bias has been acknowledged as a critical barrier for crop model simulation (Berg et al. 2010; Iizumi et al. 2009a; Ines et al. 2011, also see Chapter 4of this thesis andRamirez-Villegas et al. 2013a). Particularly for threshold-dependent model processes, there is a risk that climate model bias could trigger or prevent threshold exceedance, and in turn significantly under-

Chapter 3. Data and models 69

Table 3.4: _{CMIP5 GCMs used in the study and their main characteristics.}

Model name Ensemble members NC HRx NR1

HRy Calendar BCC-CSM1.1 § r1i1p1 128 2.8125 64 2.8125 365 BNU-ESM § r1i1p1 128 2.8125 44 4.0909 365 CCCMA-CanCM4 r[1-10]i1p1 128 2.8125 64 2.8125 365 CCCMA-CanESM2 § r[1-5]i1p1 128 2.8125 64 2.8125 365 CNRM-CM5 § r1i1p1 256 1.4063 128 1.4063 366 CSIRO-ACCESS1.0 § r1i1p1 192 1.875 145 1.2414 366 CSIRO-Mk3.6.0 § r[1-10]i1p1 192 1.875 96 1.875 365 ICHEC-EC-EARTH r[6,8]i1p1 320 1.125 160 1.125 366 INM-CM4 § r1i1p1 180 2.0 120 1.5 365 IPSL-CM5a-LR § r[1-4]i1p1 96 3.75 96 1.875 365 IPSL-CM5a-MR r1i1p1 144 2.5 143 1.2587 365 IPSL-CM5b-LR § r1i1p1 96 3.75 96 1.875 365 MIROC-ESM r1i1p1 128 2.8125 64 2.8125 366 MIROC-ESM-CHEM r1i1p1 128 2.8125 64 2.8125 366 MIROC-MIROC4h r[1-3]i1p1 640 0.5625 320 0.5625 366 MIROC-MIROC5 r1i1p1 256 1.4063 128 1.4063 365 MOHC-HadCM3 r[1-10]i1p1 96 3.75 73 2.4658 360 MOHC-HadGEM2-CC § r1i1p1 192 1.875 145 1.2414 360 MOHC-HadGEM2-ES § r1i1p1 192 1.875 145 1.2414 360 MPI-ESM-LR § r[1-3]i1p1 192 1.875 96 1.875 366 MPI-ESM-MR § r1i1p1 192 1.875 96 1.875 366 MRI-CGCM3 § r[1,5]i1p[1,2] 320 1.125 160 1.125 366 NCAR-CCSM4 § r[1,2]i1p1 288 1.25 192 0.9375 365 NCC-NORESM1-M r1i1p1 144 2.5 96 1.875 365 GFDL-ESM2G r1i1p1 144 2.5 90 2.0 365 GFDL-ESM2M r1i1p1 144 2.5 90 2.0 365

Notes: Ensemble member names as specified in Taylor et al. (2012), with r referring to

the realization (i.e. equally realistic runs but initialized with different initial conditions), i referring to the initialization method (not relevant for historical runs), and p referring to any perturbed physics ensemble. NC and NR Number of columns (NC) and rows (NR) in the climate grid. HRx and HRy refer to horizontal resolution in the x-axis (longitude, HRx) and the y-axis (latitude, HRy), in decimal degree. Calendar type refers to that used in the climate model run: 365 is a calendar without leap years, 366 is the standard Gregorian calendar (with leap year), and 360 refers to the calendar in which all months have 30 days only used by the UK MetOffice climate models. The symbol § indicates that the GCM output was also used for GLAM and EcoCrop simulations

.

or over-estimate the effects of future projected climate change (Hawkins et al., 2013a,b;

Ramirez-Villegas et al., 2013a). In addition, climate model bias could have a significant impact on threshold-dependent processes of GLAM or on suitability responses to climate in EcoCrop.

For these reasons, both raw and bias corrected simulated GCM outputs were used as inputs into GLAM and EcoCrop in this work. Bias corrected GCM output is here defined as any treatment of the raw GCM output in an attempt to make it more realistic (Hawkins et al., 2013b; Ines and Hansen,2006). Here, the definition of bias correction includes the delta method (DEL, see below and Ver Hoef 2012). Three different methods were used. The first two are based on the methodology of Hawkins et al.(2013b), who described two climate model output bias correction methods: simple bias correction (or nudging, SH) and change factor (or delta method, DEL), both of which can be applied onto means or

onto both means and variability. Here, the two methods were used only to correct for bias in the mean, without accounting for variability. This was done because the observed temperature data used here were scaled from monthly means, and thus no account of variability could be done.

The SH method used the difference between the observed and simulated climatological means in the baseline to correct the mean of the raw daily data of the GCM. The SH method, thus, produces a time series where the daily variability is that simulated by the GCM. For temperature, the arithmetic difference was used (Eq. 3.2), whereas for precipitation and solar radiation the relative differences were used (Eq. 3.3).

MSH(t) = MRAW(t) + OB−MB
(3.2) MSH(t) = MRAW(t) ∗  1 +OB−MB MB  (3.3)

where M refers to the model data and O to the observations. Time averages (i.e. clima- tological means of the period 1966-1993) are indicated by a bar above the symbol. The corrected values (subscript SH) for each day t were calculated by adding the mean bias of the model with respect to the observations in the baseline period (subscript B) to the raw climate model output (subscript RAW ), where raw is either the historical or future GCM output. Daily SH method outputs are hereafter referred to as C5-SH and were produced both for the baseline (1966-1993) and the future climate scenario (2022-2049, RCP4.5).

The DEL method is most commonly referred to in the impacts and statistics literature as the ‘delta approach’ or ‘delta method’ (Ruane et al.,2013;Ver Hoef,2012). It has been widely used to downscale climate change model simulations for input into impact studies (Ruane et al., 2013; Singh et al., 2012; Tabor and Williams, 2010). As implemented here, the method consisted of adding the GCM projected change in each variable to the observations. As for SH, DEL temperatures were calculated using the arithmetic difference (Eq.3.4), but for precipitation and solar radiation the relative difference was used instead (Eq.3.5).

Chapter 3. Data and models 71 MDEL(t) = OB(t) + MP −MB
(3.4) MDEL(t) = OB(t) ∗  1 +MP −MB MB  (3.5)

where the subscript P refers to the future projection (2022-2049 in this study) and the climatological means are indicated with a bar above respective letters. DEL corrected data are hereafter referred to as C5-DEL.

Both SH and DEL methods were independently applied for each grid cell and GCM sim- ulation (i.e. correction factors varied spatially). Correction factors were in both cases derived for each month and then applied to daily values. For a more complete description and analysis of these two methods and a review of other methods the reader is referred to

Hawkins et al. 2013a,b.

The last method used here is called local-intensity scaling (LOCI) and is classified as an ‘empirical-statistical downscaling and error correction method’ (Schmidli et al.,2006;

Themessl et al., 2011). The technique consists in correcting both wet-day intensity and frequency. In other words, it corrects biases in the number of rainy days and in the total precipitation falling in such days. The underlying assumption in LOCI is that climate model precipitation integrates all relevant predictors. Therefore, to apply LOCI to a given model simulation, other climate fields are irrelevant (Themessl et al., 2011). This means that solar radiation and temperatures are not corrected. Although this assumption may not hold valid under a number of conditions (Ehret et al., 2012;Piani and Haerter,

2012;Themessl et al.,2012), LOCI has been found to be amongst the best performing bias correction techniques (Ehret et al.,2012;Themessl et al.,2011). Since LOCI corrects using parameters that are valid over a sufficiently long period of time (e.g. 30-year climatology), it is capable of correcting both numerical weather predictions and transient climate change simulations (Schmidli et al.,2006; Themessl et al.,2011).

On a monthly basis, two parameters were estimated: the model wet-day threshold (W Tmod₎

and the scaling factor (S). First, W Tmod _{was estimated as the threshold above which the}

number of wet days predicted by the model equalled the number of wet days in the obser- vations. The number of wet days in the observations is hereby defined following Schmidli

et al.(2006) as the number of days above a threshold W Tobs _{of 1 mm day}−1 _{(also seeNew} et al. 2000). Next, S was estimated using Eq.3.6.

St,i =

P W Dobs

t,i −W Tt,iobs

P W Dmod

t,i −W Tt,imod

(3.6)

where P W D is the climatological mean of wet days for observations (obs) and GCM (mod). P W D is calculated for days above the respective W T threshold. The scaling factor is calculated for each location (i) and for each month in the year (t), and is a single value representing the whole baseline period. The monthly correction factor and the W Tmod threshold are then used to correct the intensity and frequency of each month in both the baseline and the future GCM simulations. As with the SH method, there is an assumption that the model bias stays constant or has negligible variation through time. Given that the analyses presented here focus on the 2030s, this assumption is unlikely to bias the results presented (see e.g. Hawkins et al. 2013a). LOCI-corrected data are termed C5-LOCI.

All methods were applied at the resolution of the TS IMD-GM dataset (1x1 degree) and thus there was some degree of downscaling involved in the application of the three tech- niques (Hawkins et al.,2013b). The resulting datasets were all at daily scale for the periods 1966-1993 and 2022-2049.

Bias corrected data were also used for EcoCrop suitability simulations. Since EcoCrop uses monthly climatological means, daily precipitation and mean, maximum and minimum surface temperature were totalised or averaged over each month and then averaged over the entire baseline (1966–1993) and future scenario (2022–2049) periods in order to obtain bias- corrected GCM climatological means for C5-SH, -DEL and -LOCI (see Table3.1). Because the climatological means of the DEL and BC methods are mathematically equivalent (see

Hawkins et al. 2013b), this reduced EcoCrop bias corrected inputs to 2 (DEL and LOCI) as opposed to the 3 used for GLAM (SH, DEL, LOCI). Since EcoCrop did not make use of solar radiation data, no further processing was done for that variable.

Chapter 3. Data and models 73