Sources of uncertainty in future changes in local precipitation

Abstract

This study considers the large uncertainty in projected changes in local precipitation. It aims to map, and begin to understand, the relative roles of uncertain modelling and natural variability, using 20-year mean data from four perturbed physics or multi-model ensembles. The largest—280-member—ensemble illustrates a rich pattern in the varying contribution of modelling uncertainty, with similar features found using a CMIP3 ensemble (despite its limited sample size, which restricts it value in this context). The contribution of modelling uncertainty to the total uncertainty in local precipitation change is found to be highest in the deep tropics, particularly over South America, Africa, the east and central Pacific, and the Atlantic. In the moist maritime tropics, the highly uncertain modelling of sea-surface temperature changes is transmitted to a large uncertain modelling of local rainfall changes. Over tropical land and summer mid-latitude continents (and to a lesser extent, the tropical oceans), uncertain modelling of atmospheric processes, land surface processes and the terrestrial carbon cycle all appear to play an additional substantial role in driving the uncertainty of local rainfall changes. In polar regions, inter-model variability of anomalous sea ice drives an uncertain precipitation response, particularly in winter. In all these regions, there is therefore the potential to reduce the uncertainty of local precipitation changes through targeted model improvements and observational constraints. In contrast, over much of the arid subtropical and mid-latitude oceans, over Australia, and over the Sahara in winter, internal atmospheric variability dominates the uncertainty in projected precipitation changes. Here, model improvements and observational constraints will have little impact on the uncertainty of time means shorter than at least 20 years. Last, a supplementary application of the metric developed here is that it can be interpreted as a measure of the agreement amongst models of their projected local precipitation change. Results differ from, but are complementary to, those of the more usual approach.

Appendices

Appendix 1: CMIP3 models

The AO-MME ensemble, described in Sect. 2.4, comprises the following 16 models (from 12 institutes):

• Canadian Centre for Climate Modelling and Analysis coupled GCM, version 3.1, at T47 and T63 resolutions (CGCM3.1-T47 and CGCM3.1-T63)

• Geophysical Fluid Dynamics Laboratory coupled model versions 2.0 and 2.1 (GFDL-CM2.0 and GFDL-CM2.1)

• Goddard Institute for Space Studies model GISS-EH

• Institute of Atmospheric Physics model FGOALS-g1.0

• Institute of Numerical Mathematics coupled model version 3.0 (INM-CM3.0)

• JAMSTEC (Center for Climate System Research, National Institute for Environmental Studies, and Frontier Research Center for Global Change) model for interdisciplinary research on climate, version 3.2, with medium-resolution (MIROC3.2-medres)

• Met Office Hadley Centre models HadCM3 and HadGEM1

• Météo-France Centre National de Recherches Météorologiques model version 3 (CNRM-CM3)

• Meteorological Institute of the University of Bonn (MIUB) and Meteorological Research Institute of KMA (METRI) model MIUB-ECHO-G

• Max Planck Institute model MPI-ECHAM5

• Meteorological Research Institute coupled GCM version 2.3.2 (MRI-CGCM2.3.2)

• National Center for Atmospheric Research (NCAR) models CCSM3 and PCM1

Appendix 2: Estimation of natural variability

Two sources of sampling error contribute to inaccurate estimates of R. One is inadequate sampling of model formulations, and the other is inadequate sampling of natural variability. The former is an issue in all but one of the ensembles analysed here (the exception being the AS-PPE-A ensemble), and its impact is discussed in Sects. 4 and 5. The latter—natural variability—is likely to be a problem in all ensembles, but nevertheless there are potential strategies to limit it. These depend on the experimental structure of each ensemble, and are described here.

2.1 AS-PPE-A

For the large slab model ensemble, M = 280, N_Cntl = 20 and N_Fut = 20 (Sect. 2.1). Ideally, much longer control and doubled-CO₂ integrations would be available for each model, from which reliable estimates of $\sigma_{{{\text{NatCntl}}\,{\text{m}}}}^{2}$ and $\sigma_{{{\text{NatFut}}\,{\text{m}}}}^{2}$ could be provided. Clearly, this is computationally impractical. However, 600-year integrations are available for the control and doubled-CO₂ runs of the standard model, providing a choice of two possible approaches.

First, good estimates of $\sigma_{{{\text{NatCntl}}\,20}}^{2}$ and $\sigma_{{{\text{NatFut}}\, 2 0}}^{2}$ could be computed for the standard model from these 600-year integrations, and then the assumption made that the natural variability of the remaining 279 models is very similar to that of the standard model.

Second, $\sigma_{{{\text{NatCntl}}\,{\text{m}}\,20}}^{2}$ and $\sigma_{{{\text{NatFut}}\,{\text{m}}\, 2 0}}^{2}$ for each model could be estimated from the interannual variability of their control and doubled-CO₂ integrations:

$$ \hat{\sigma }^{2}_{{{\text{NatCntl}}\,{\text{m}}\,20}} \approx \frac{1}{20}\hat{\sigma }^{2}_{{{\text{NatCntl}}\,{\text{m}}\,1}} \quad {\text{where}}\quad \hat{\sigma }^{2}_{{{\text{NatCntl}}\,{\text{m}}\,1}} = \frac{1}{20}\sum\limits_{i = 1}^{20} {\left( {P_{{{\text{i}}\,{\text{m}}}} - \overline{{P_{\text{m}} }} } \right)^{2} } $$

where $\hat{\sigma }^{2}_{{{\text{NatCntl}}{\kern 1pt} {\text{m}}{\kern 1pt} 1}}$ is the natural variability of single seasons from the control integration of model m. A similar calculation would estimate $\sigma_{{{\text{NatFut}}\,{\text{m}}\,20}}^{2}$. This necessitates the assumption that the internal climate variability of these runs approximates to a white noise process.

The relative merit of these two approaches was assessed by comparing them with a further estimate computed from the interannual variability of the 600-year standard model integrations (i.e. making the assumptions of both the above approaches). This showed that the large-scale pattern of variability is affected more by removing the estimates of other models than it is by assuming an approximate white noise process. This is due to large inter-model variability in the mean and variance of precipitation, which cannot be represented by a single model, particularly in the dry subtropics. Thus, the second approach above was chosen, i.e. to estimate $\sigma_{{{\text{NatCntl}}\,{\text{m}}\,20}}^{2}$ and $\sigma_{{{\text{NatFut}}\,{\text{m}}\, 2 0}}^{2}$ using the interannual variance of all 280 models.

2.2 AO-PPE-A and AOC-PPE-C

For the two coupled model PPEs, M = 17, N_Fut = 40, and N_Cntl is either 150 or 240 (for AO-PPE-A and AOC-PPE-C, respectively; Sects. 2.2, 2.3).

First, the natural variability of 20-year means, $\hat{\sigma }^{2}_{{{\text{NatCntl}}{\kern 1pt} {\text{m}}{\kern 1pt} 20}}$, required in Eq. 5, can be computed directly from the control experiment of each model. Although these variances are necessarily estimated from rather small samples (7 and 12 independent 20-year means for AO-PPE-A and AOC-PPE-C, respectively), we note that much of this sampling error is removed by computing their multi-model mean (Eq. 5).

Next, natural variances of the 150 or 240-year control means are required to estimate $\hat{\sigma }^{2}_{\text{Model}}$ as a residual from Eqs. 3b and 3a. These are estimated from $\hat{\sigma }^{2}_{{{\text{NatCntl}}{\kern 1pt} {\text{m}}{\kern 1pt} 20}}$ by assuming that internal climate variability approximates to a white noise process at longer timescales. Thus:

$$ \hat{\sigma }^{2}_{{{\text{NatCntl}}\,{\text{m}}\,150}} \approx \frac{20}{150}\hat{\sigma }^{2}_{{{\text{NatCntl}}\,{\text{m}}\,20}} \quad {\text{and}}\quad \hat{\sigma }^{2}_{{{\text{NatCntl}}\,{\text{m}}\,240}} \approx \frac{20}{240}\hat{\sigma }^{2}_{{{\text{NatCntl}}\,{\text{m}}\,20}} $$

where $\hat{\sigma }^{2}_{{{\text{NatCntl}}{\kern 1pt} {\text{m}}{\kern 1pt} 150}}$ and $\hat{\sigma }^{2}_{{{\text{NatCntl}}{\kern 1pt} {\text{m}}{\kern 1pt} 240}}$ are the estimated natural variability of 150 and 240-year means in the pre-industrial climate of model m.

Last, the natural variances of 40-year scenario means are required in Eq. 3b. However, equilibrium simulations are not available with enhanced anthropogenic emissions, since this would be computationally expensive for 17 models. Therefore, we consider two alternative approaches, with differing assumptions. One is to detrend the 40 years of scenario data used to compute the precipitation anomalies. However, this approach may not reliably isolate natural variability, and would also increase random errors due to small sample sizes of both years and models. The alternative approach, adopted here, is to utilise the data of the long control integrations, and assume that the natural variability of climate means under enhanced emissions is similar to that of the pre-industrial era. Thus:

$$ \hat{\sigma }^{2}_{{{\text{NatFut}}\,{\text{m}}\,40}} \approx \frac{20}{40}\hat{\sigma }^{2}_{{{\text{NatCntl}}\,{\text{m}}\,20}} $$

A sensitivity analysis using the large AS-PPE-A ensemble (not shown) demonstrates that replacing $\sigma_{{{\text{NatFut}}\,{\text{m}}}}^{2}$ in this way has only a limited impact on the pattern of R.

2.3 AO-MME

For this ensemble, M = 16, and N_Cntl = N_Fut = 79. Computational details are the same as those used for AO-PPE-A and AOC-PPE-C, except that a few minor adjustments are required because a number of models experience notable drift in their mean climate.

To compute the time-mean anomalies in projected precipitation (Eq. 1), the period chosen from the control integration of each model was that starting at the date from which the scenario integration was initiated. The first 70 years of data were then removed from both experiments (during which CO₂ rises towards stabilisation in the scenario experiment). Time-mean anomalies were then computed from the following 79 years (note that additional years were not used from the control experiment to avoid the impact of continuing climate drift on the computed anomalies).

To estimate the natural variability of 20-year means (required in Eq. 5), data from the full length of each model’s control experiment is used, after first removing a linear trend at each grid-box. Natural variances of 79-year means in the control and doubled-CO₂ climates are then estimated from this detrended control data using the same approach as for the coupled model PPE data.