Fine-Scale Climate Projections: What Additional Fixed Spatial Detail Is Provided by a Convection-Permitting Model?

David P. Rowell aMet Office Hadley Centre, Exeter, United Kingdom

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Ségolène Berthou aMet Office Hadley Centre, Exeter, United Kingdom

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Abstract

Convection-permitting (CP) models promise much in response to the demand for increased localization of future climate information: greater resolution of influential land surface characteristics, improved representation of convective storms, and unprecedented resolution of user-relevant data. In practice, however, it is contended that the benefits of enhanced resolution cannot be fully realized due to the gap between models’ computational and effective resolution. Nevertheless, where surface forcing is strongly heterogeneous, one can argue that usable information may persist close to the grid scale. Here we analyze a 4.5-km resolution CP projection for Africa, asking whether and where fine-scale projection detail is robust at sub-25-km scales, focusing on geolocated rainfall features (rather than Lagrangian motion). Statistically significant detail for seasonal means and daily extremes is most frequent in regions of high topographic variability, most prominently in East Africa throughout the annual cycle, West Africa in the monsoon season, and to a lesser extent over Southern Africa. Lake coastal features have smaller but significant impacts on projection detail, whereas ocean coastlines and urban conurbations have little or no detectable impact. The amplitude of this sub-25-km projection detail can be similar to that of the local climatology in mountainous regions (or around a third near East Africa’s lake shores), so potentially beneficial for improved localization of future climate information. In flatter regions distant from coasts (the majority of Africa), spatial heterogeneity can be explained by chaotic weather variability. Here, the robustness of local climate projection information can be substantially enhanced by spatial aggregation to approximately 25-km scales, especially for daily extremes and equatorial regions.

Significance Statement

Recent substantial increases in the horizontal resolution of climate models bring the potential for both more reliable and more local future climate information. However, the best spatial scale on which to analyze such data for impacts assessments remains unclear. We examine a 4.5-km resolution climate projection for Africa, focusing on seasonal and daily rainfall. Spatially fixed fine-scale projection detail is found to be statistically robust at sub-25-km scales in the most mountainous regions and to a lesser extent along lake coastlines. Elsewhere, the model data may be better aggregated to at least 25-km scales to reduce sampling uncertainties. Such evolving guidance on the circumstances and extent of high-resolution data aggregation will help users gain greater benefit from climate model projections.

For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: David Rowell, dave.rowell@metoffice.gov.uk

Abstract

Convection-permitting (CP) models promise much in response to the demand for increased localization of future climate information: greater resolution of influential land surface characteristics, improved representation of convective storms, and unprecedented resolution of user-relevant data. In practice, however, it is contended that the benefits of enhanced resolution cannot be fully realized due to the gap between models’ computational and effective resolution. Nevertheless, where surface forcing is strongly heterogeneous, one can argue that usable information may persist close to the grid scale. Here we analyze a 4.5-km resolution CP projection for Africa, asking whether and where fine-scale projection detail is robust at sub-25-km scales, focusing on geolocated rainfall features (rather than Lagrangian motion). Statistically significant detail for seasonal means and daily extremes is most frequent in regions of high topographic variability, most prominently in East Africa throughout the annual cycle, West Africa in the monsoon season, and to a lesser extent over Southern Africa. Lake coastal features have smaller but significant impacts on projection detail, whereas ocean coastlines and urban conurbations have little or no detectable impact. The amplitude of this sub-25-km projection detail can be similar to that of the local climatology in mountainous regions (or around a third near East Africa’s lake shores), so potentially beneficial for improved localization of future climate information. In flatter regions distant from coasts (the majority of Africa), spatial heterogeneity can be explained by chaotic weather variability. Here, the robustness of local climate projection information can be substantially enhanced by spatial aggregation to approximately 25-km scales, especially for daily extremes and equatorial regions.

Significance Statement

Recent substantial increases in the horizontal resolution of climate models bring the potential for both more reliable and more local future climate information. However, the best spatial scale on which to analyze such data for impacts assessments remains unclear. We examine a 4.5-km resolution climate projection for Africa, focusing on seasonal and daily rainfall. Spatially fixed fine-scale projection detail is found to be statistically robust at sub-25-km scales in the most mountainous regions and to a lesser extent along lake coastlines. Elsewhere, the model data may be better aggregated to at least 25-km scales to reduce sampling uncertainties. Such evolving guidance on the circumstances and extent of high-resolution data aggregation will help users gain greater benefit from climate model projections.

For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: David Rowell, dave.rowell@metoffice.gov.uk

1. Introduction

Regional climate projections utilizing high-resolution convection-permitting (CP) models are becoming increasingly available (Prein et al. 2015; Kendon et al. 2021; Lucas-Picher et al. 2021; Senior et al. 2021). Their improved representation of convection brings demonstrable improvements to the distribution of rainfall intensity (e.g., Berthou et al. 2019b; Ban et al. 2021), and so also some aspects of the representation of historical mean climate (e.g., Hart et al. 2018; Finney et al. 2019), together contributing to greater trust in the mechanisms of future change (e.g., Jackson et al. 2020, 2022; Prein et al. 2017; Dai et al. 2020; Rasmussen et al. 2020; Poujol et al. 2021). Furthermore, the unprecedented horizontal resolution of such simulations, typically 2–5 km, brings enhanced spatiotemporal detail (Crook et al. 2019; Prein et al. 2020) with the potential to provide more reliable localized information on future climate. Such information is much in demand from users, particularly those affected by the location-specific effects of land–water discontinuities, urban–climate interactions, and topographic variability.

In the physical climate science community, discussion of the advantages of CP modeling has primarily focused on the benefits of replacing convective parameterization with an explicit representation founded on the model dynamics. Enhanced model resolution is viewed partly as a strategy toward improving the representation of convection and its feedbacks onto larger scales. Furthermore, the community is rightly cautious about employing model data close to its computational resolution because it is well known that a model’s “effective resolution” (below which numerical effects may become apparent) is somewhat coarser than its grid scale (Pielke 1991; Skamarock 2004; Klaver et al. 2020). This issue becomes apparent in grid-scale rainfall data, which can either be too intense at too small spatiotemporal scales, or not intense enough, depending on the model used (Stein et al. 2014; Berthou et al. 2019b; Fumière et al. 2020).

For impact studies, these issues can be resolved by spatial aggregation of model data (hereafter, “aggregation” is used as a generic term to encompass spatial averaging or spatial pooling). In historical simulations, such aggregation is found to substantially improve verification against observed distributions of rainfall intensity (Berthou et al. 2019b; Fumière et al. 2020). In this study we consider spatial aggregation to a 25-km scale because this is several times the grid length of our model, has been applied to the same simulations in recent studies (e.g., Finney et al. 2020; Wainwright et al. 2021; Mittal et al. 2021), and is now a primary target resolution for the Coordinated Regional Climate Downscaling Experiment (CORDEX; CORDEX 2021).

In contrast, the climate application community may prefer direct use of the high-resolution data available from CP models because stakeholders and policy makers inevitably face the challenge of providing future climate change information on a location-by-location basis (e.g., Mittal et al. 2021; Orr et al. 2021). Interdisciplinary discussions—in our experience in the “Future Climate for Africa” program—have therefore revealed different perspectives on the value of CP experiments, with some emphasizing the importance of the improved representation of convection and others emphasizing the importance of the unprecedented resolution of the projected climate data.

This raises critical questions about the usable spatial scales of such projections, and so our objective is to begin to provide guidance on this topic. We focus on geographically fixed spatial detail, aiming to help develop best practice for users at specific locations, as opposed to better understanding the underlying improvements in storm morphology. Thus, we focus on Eulerian statistics, rather than Lagrangian statistics [research on the latter is provided by studies such as those of Prein et al. (2017), Fitzpatrick et al. (2020), and Poujol et al. (2020)].

This kind of fine spatial detail in future climate change information will be most likely apparent—and therefore of greatest potential benefit to users—where surface forcing is most heterogeneous, such as mountain, coastal, and urban regions. These benefits could manifest despite the aforementioned biases in rainfall intensity, which could be corrected via statistical postprocessing. Conversely, in regions of homogeneous surface forcing, fine-scale variability is likely dominated by small-scale chaotic variability, and hence aggregation of local results would reduce sampling uncertainty, so providing more robust information.

This study focuses on two overarching questions. First, is there is any robust fine-scale spatial variability in projection anomalies at sub-25-km scales (i.e., beyond that due to fine-scale chaotic variability)? This provides the higher-resolution detail demanded by users. We hereafter describe this as fine-scale projection detail (FSPD, in this case without a suffix for qualitative meaning; mathematical quantities are defined later; see Table 1). To be clear, we address future climate anomalies rather than the more often addressed present-day detail, and we focus on geographically fixed FSPD. If the answer to this first question is affirmative, this raises subsidiary questions as follows. How widespread is this FSPD? Where is it found, are any regional or seasonal patterns apparent, and what are the relative roles of topographic, coastal, and urban features? Is the magnitude of FSPD large enough to make any real difference to users? In contrast, our second key question examines locales with no significant fine-scale projection detail (i.e., where sub-25-km scale spatial variability is dominated by chaotic weather variability and numerical effects within the model’s dynamics and parameterizations) and asks: What is the extent to which uncertainty in local projections can be reduced if data are first spatially aggregated for users?

Table 1

Definitions.

Table 1

We focus on the vulnerable continent of Africa, utilizing a pair of unique pan-Africa CP model simulations of recent and future climate, with a horizontal resolution of 4.5 km. The domain encompasses a range of climates, from equatorial to subtropical, with diverse weather system characteristics, and varied topographic, lake, ocean, and urban influences. It is hoped, therefore, that the methods developed in this study may be globally applicable. We address the above questions with a focus on geolocated projected rainfall changes, both seasonal means and daily extremes, each of which may be expected to exhibit heterogeneous climate responses to sharp gradients in surface forcing, and furthermore are critical ingredients of lives and livelihoods across Africa. Last, we note our language is deliberately framed as addressing fine-scale projection detail rather than added value. The latter adds an inference of trust in the fine-scale detail, which, although also critical for users, is beyond the scope of this initial study, not least because it must be addressed for each locality of interest, which will be shown to be challenging with the data available here.

In section 2 we describe the CP simulations used in this study, the surface data used to derive the candidate forcings of FSPD, and the statistical methodology. Robust statistical treatment is particularly important due to the relatively short duration of the simulations, due in turn to their considerable expense. Section 3 evaluates the extent of statistical significance of FSPD in the simulations available here (against a null hypothesis of chaotic weather variability), its spatial and seasonal patterns, and in particular the relative roles of topographic, coastal, and urban features. Section 4 examines the magnitude of the FSPD where it is statistically significant, and conversely section 5 examines the benefits of aggregation where FSPD is insignificant. Conclusions are presented in section 6.

2. Data and statistical approaches

a. Model simulations

This study utilizes a pair of simulations from a convection-permitting model (the Met Office Unified Model) run over a pan-Africa domain (45°S–40°N, 25°W–56°E; Fig. 1), hereafter referred to as CP4A. The model has a horizontal resolution of 4.5 km at the equator, with 80 levels in the vertical, and convection explicitly represented using the model dynamics. Ocean and lake surface temperatures are specified (i.e., are noninteractive). Further details are provided by Stratton et al. (2018) and Senior et al. (2021).

Fig. 1.
Fig. 1.

Maps of CP4A (a) topographic height (m), (b) local topographic standard deviation (m) (defined in section 2b and Table 1), and (c) distance from the nearest large urban conurbation (smoothed urban fraction > 0.1). All data are averaged to a 0.25° scale for plotting. Boxes show the three subcontinental regions.

Citation: Journal of Climate 36, 4; 10.1175/JCLI-D-22-0009.1

The Control (or historical) experiment—described in detail by Stratton et al. (2018)—simulates the period January 1997–February 2007, forced by observed sea and lake surface temperature data (Reynolds et al. 2007; Hook et al. 2012, respectively). Atmospheric greenhouse gas concentrations are updated annually, and aerosol concentrations are fixed. Lateral boundary conditions derive from a similarly forced global atmosphere-only simulation with ∼25-km resolution.

The Future experiment simulates a 10-yr period circa 2100, and is described by Kendon et al. (2019). Ocean surface forcing uses the same observed data with the addition of an annual cycle of anomalies for 2085–2115 from the fully coupled HadGEM2-ES projection forced by the representative concentration pathway 8.5 (RCP8.5) emissions scenario. Lateral boundary data again derive from a similarly forced global atmosphere-only simulation, which also provides land surface temperatures to compute lake surface temperature anomalies with the addition of an inertial term (see also Finney et al. 2020). Greenhouse gas concentrations use 2100 data from the RCP8.5 scenario, and aerosol concentrations remain the same as the Control experiment.

b. Surface forcings

The impact of three sources of temporally invariant surface forcing on FSPD are considered. First, topography. In CP4A this derives from the Global Land One-kilometer Base Elevation (GLOBE) dataset (Hastings et al. 1999), and was smoothed at the grid scale for numerical stability (but with very little damping at 25-km scales; Webster et al. 2003). Here, fine-scale topographic variability is measured as the standard deviation of elevation across a rolling window of 5 × 5 grid boxes centered on every CP4A grid box, so commensurate with our 25-km aggregation scale (Table 1). Figure 1b shows that CP4A’s topographic variability delineates mountainous regions, not only from low-lying areas, but also from the large-scale plateaus of Southern Africa and northern West Africa seen in Fig. 1a. Note that the model topography and land–sea mask were inadvertently offset by half a grid length from reality (Senior et al. 2020), so for consistent analysis all computations in this study use the grid seen by the model.

Second, the impact of coastal features is considered by computing the proximity of every grid box to its nearest coastline. The smallest lakes, and all but the broadest rivers, are excluded for this purpose by removing land/water discontinuities where the surrounding 11 × 11 grid boxes (∼50 × 50 km) are less than 20% water. Lake versus sea coastlines are discriminated by their Boolean match to zero altitude. The potential for conflating effects of topographic variability (e.g., a lake situated in a mountainous region) is largely eradicated by replacing coastal distance at any grid box with missing data if its local topographic standard deviation exceeds 100 m. Conclusions were found to be insensitive to the values of each of the above thresholds.

Third, CP4A’s urban fraction was determined from the satellite-derived Climate Change Initiative land cover (CCI-LC) dataset (Poulter et al. 2015) that classifies global terrestrial pixels at 300-m resolution. The CCI-LC urban class was pooled to an urban fraction on the CP4A grid, with maximum values of 0.75 (cf. Hartley et al. 2017). Two approaches are used to examine the impact of urban settlements on FSPD. Our focus is on an approach analogous to coastal features, whereby the proximity of every grid box to the nearest large city is computed (Fig. 1c). These are defined as grid boxes with an average urban fraction exceeding 0.1 over the surrounding 5 × 5 boxes. A total of 86% of these ∼25-km-scale urban areas contain at least one grid-scale box with an urban fraction exceeding 0.3, and 54% contain at least one box exceeding 0.6. To reduce conflation between urban, coastal, and topographic effects, grid boxes less than 50 km from any coastline or with local topographic standard deviation greater than 100 m are excluded from the urban analysis in section 3c. Little sensitivity to these thresholds is found. For comparison, a second approach—analogous to the evaluation of topographic features—was also employed, whereby fine-scale urban heterogeneity is computed as the standard deviation of urban fraction across 5 × 5 grid boxes centered on every CP4A grid box.

c. Rainfall metrics, regions, and seasons

Analysis of FSPD focuses on two metrics: seasonal mean rainfall (Pseas) and the intensity of extreme daily rain events (P99), the latter measured by the 99th percentile of all days in a given season (again, reminders of all definitions appear in Table 1). We use daily data for extreme events, partly because this is the most common observational time scale, and partly because it circumvents CP4A’s excessive localization of rainfall at very short spatiotemporal scales (Berthou et al. 2019b). We recognize, however, that application to localized flash flooding will motivate subsequent analysis at shorter time scales.

The analysis of sections 35 necessitates pooling of local results across large subcontinental regions to enhance statistical sampling. Three climatologically distinct regions are defined by the boxes in Fig. 1: West Africa and Southern Africa, with their differing unimodal seasonal cycles, and East Africa with its bimodal seasonality. The seasons on which we then focus are determined by the annual cycles of these regions: March–May (MAM) and October–December (OND) are the wet seasons of East Africa, July–September (JAS) is the wet season of West Africa, and December–February (DJF) is the wettest season over Southern Africa (Fig. 2). Last, for all analysis, only data over land and lakes are analyzed.

Fig. 2.
Fig. 2.

Maps of CP4A Control climatological rainfall (mm day−1), averaged over all years. Data are averaged to a 1° scale for plotting. Boxes show the three subcontinental regions.

Citation: Journal of Climate 36, 4; 10.1175/JCLI-D-22-0009.1

d. Significance testing of fine-scale projection detail

To address our first research question—whether and where FSPD can be detected above fine-scale chaotic variations—we require a statistical significance test of the null hypothesis of zero FSPD. This subsection describes our approach, with Table 1 providing a reference for terminology.

Projected anomalies in seasonal mean rainfall and extreme rainfall intensity are first computed as ΔR = Future/Control. A ratio calculation is chosen because the zero-bounded nature of rainfall causes its absolute anomalies to be to roughly proportional to its underlying climatology, so the ΔR approach excludes FSPD arising merely from climatological heterogeneity.

The spatial heterogeneity of ΔR is then computed at the two length scales within the 25-km scale considered here (in other words, together they act as a high-pass spatial filter). At the scale of CP4A’s native grid, the difference between ΔR in neighboring grid boxes is computed using each box’s eight adjacent neighbors, each difference defining a value of FSPDND (e.g., ΔRPseasi − ΔRPseasj, where i and j are adjacent grid boxes). At the 3-grid-length scale (i.e., ∼13 km) daily rainfall data are first smoothed by averaging across a rolling window of 3 × 3 grid boxes, then the seasonal mean and extreme rainfall statistics recomputed, along with their ΔR, and finally FSPDND computed as the difference between ΔR in adjacent 3 × 3 boxes (i.e., box centers 3 grid lengths apart).

To detect FSPDND beyond heterogeneities due to its inclusion of small-scale chaotic variability, its statistical significance is computed. The null hypothesis (H0) is that two neighboring ΔR derive from the same population (this being a hypothetical pair of CP experiments of infinite duration and/or ensemble size). Candidate statistical approaches should be carefully examined because any bias in the rejection rate of H0 will confound our interpretation of FSPD in circumstances of marginal statistical significance, which may be more likely given the relative short duration of the CP4A simulations. Therefore the appendix formulates a conceptual model to provide large quantities of synthetic daily rainfall data, from which test bias and power are computed across a wide variety of climate characteristics.

For rainfall extremes, the P99 statistic is strongly skewed, invalidating the Gaussian assumption required for parametric testing. We therefore consider the bootstrapping approach of Chan et al. (2020). Data for a given season are resampled from the ten 90-day blocks with replacement (using identical resampling for the Control and Future due to their matching interannual oceanic forcing), P99 is recomputed, and new ΔR and near-neighbor differences (FSPDND) are computed. This is repeated 1000 times, and the mean of these bootstrapped metrics subtracted so as to derive an approximate zero-centered probability distribution of FSPDND under H0. The original (non-resampled) FSPDND is then judged statistically significant at the 10% level if it lies outside the 5th–95th percentile range of this resampled distribution. Independence of years (i.e., that multiyear differences within 1997–2006 are not clearly distinct from interannual variability) is assumed, which appears valid from a visual assessment of published time series (e.g., Rowell et al. 2015; Nicholson 2018). The performance of this bootstrapping approach has not been previously assessed, but for its application to FSPD of rainfall extremes, the appendix suggests that its rejection of H0 is mostly well behaved. It is typically found to be marginally conservative (slightly too few rejections under H0), with the important exception of more substantial bias in arid regions.

For seasonal mean rainfall, we evaluate a parametric significance test alongside the bootstrap test, since the distribution of Pseas may be sufficiently indistinct from Gaussian, especially with few years of data. A paired-difference t test is applied to the samples of 10 years of ΔR between neighboring grid boxes due to their partial dependence (e.g., von Storch and Zwiers 1999), and the appendix compares its bias and power with the bootstrapping approach. The paired-difference test performs well, as expected from its well-documented efficacy under broadly valid assumptions, again with the exception of arid environments where it is strongly conservative, likely due to violation of the Gaussian assumption. In comparison, with a sample of only 10 years, the bootstrap test rejects H0 too easily in most climates, and has a similar conservative bias to the parametric test in arid region seasons. Thus in the following sections, we employ the parametric testing for seasonal mean data.

Last, to avoid contamination from the substantive test bias in arid regions, we set all significance rates to missing data in seasons and locations where the Control seasonal climatology is less than 1 mm day−1. This threshold aims to balance the competing demands of minimizing test bias and data exclusion, but in any case sensitivity analysis (not shown) finds our conclusions to be robust to a doubling of the threshold.

3. Impacts of surface forcing on the statistical significance of fine-scale projection detail

To examine the extent and distribution of FSPD in CP4A, Fig. 3 maps the fraction of statistically significant FSPDND (hereafter “fractional FSPDND significance”; Table 1) for seasonal mean rainfall and the intensity of daily extremes, after first smoothing daily data to the 3-grid-length scale. Color scales are centered on the expected rejection rate under H0, accounting for the slight test bias for extremes (see the appendix). For both metrics, the overall impression is of slightly higher fractional FSPDND significance than the value of ∼0.1 expected by chance, suggesting that field significance is weak across sub-Saharan Africa. Areas of unrealistically low significance rates likely reflect poor test performance in arid margins (section 2d and Fig. 2). Elsewhere, a few regions of enhanced significance are apparent for seasonal mean rainfall (rejection rates exceeding 20%), potentially reflecting seasonally varying fine-scale impacts from the mountains of East Africa and the Cameroon Highlands.

Fig. 3.
Fig. 3.

Maps of the fraction of CP4A statistically significant fine-scale projection detail (fractional FSPDND significance), at the 10% level, computed for each 1° box, for (left) seasonal mean rainfall and (right) the 99th percentile of daily rainfall intensity. The analysis uses data first smoothed to a 3-grid-length scale. The right-hand color scale is shifted to center on the 9% null hypothesis rejection rate found in the conceptual model (yellow). Arid regions (climatology < 1 mm day−1) vulnerable to significance bias are masked (white).

Citation: Journal of Climate 36, 4; 10.1175/JCLI-D-22-0009.1

Spatial heterogeneity in Fig. 3 is nevertheless high, with few clear patterns that might link to surface features. This suggests a strong impact on significance rates from random sampling of small-scale variability, implying that the CP4A simulations are likely too short to examine FSPD at most individual locations. Nevertheless, there may be sufficient significant neighboring pairs across large regions to make broad statements about typical links between the extent of FSPD and the amplitude of surface features, such as topographic variability, coastlines, and urban conurbations. These are examined in each of the following subsections.

a. Topographic impacts

Figure 4 examines the impact of fine-scale topographic variability on the fraction of significant fine-scale detail in the projection data. Analysis is pooled across each large-scale African region and each season. Grid boxes are binned according to their fine-scale topographic variability, using 40-m bin sizes in less mountainous regions and thereafter increasing nonlinearly to maintain at least 100 grid box pairs per bin. All neighboring pairs associated with the grid boxes in a given bin are used to compute a percentage of significant projection differences (at the 10% level), which is plotted against the mean topographic variability of that bin (sloping lines). Comparative rejection rates under the null hypothesis of zero FSPDND (horizontal lines) are either set at 10% for seasonal means, or computed from the conceptual model for extremes, forced by parameters derived from CP4A data for each region-season.

Fig. 4.
Fig. 4.

Impact of topographic variability on the fraction of CP4A statistically significant fine-scale projection detail (fractional FSPDND significance; left-hand axis), at the 10% level, for seasonal mean rainfall (solid lines) or the 99th percentile of daily rainfall intensity (dashed lines), at the 3-grid-length scale (thick lines) or on the native grid (thin lines). Topographic variability bin sizes increase nonlinearly, with fractional significance plotted against the mean topographic variability of each bin. Horizontal lines show the estimated rejection rate under the null hypothesis (solid or dashed for seasonal or extreme rain, respectively). Shading (right-hand axis) shows analyzed grid box counts in evenly spaced 40-m topographic variability bins. Arid regions (climatology < 1 mm day−1) are excluded, and DJF in West Africa has too few eligible grid boxes to analyze.

Citation: Journal of Climate 36, 4; 10.1175/JCLI-D-22-0009.1

In flat regions (left-hand end of all lines), not surprisingly, little or no FSPDND is detected for both metrics and both spatial scales, with rejection rates close to those expected by chance under H0. Thus, no significant projection detail is lost from the short CP4A simulations if data in flat environments (which account for a substantial portion of the landmass of sub-Saharan Africa; see shading) are first aggregated to ∼25-km scales.

With increasing topographic variability, and focusing first on seasonal means at the 3-grid-length scale (thick solid lines), the prevalence of significant FSPDND notably increases as the terrain becomes more mountainous. In these environments, sub-25-km scale information is therefore more robust and potentially usable for impacts assessments that need to address these fine scales. However, such usability also requires sufficient amplitude of FSPD (to be evaluated in section 4), the correction of any distributional bias in fine-scale rainfall, and an understanding of the trustworthiness of local anomaly patterns. This seasonal rainfall FSPDND is most notable throughout the annual cycle over East Africa (where topographic variability is largest), for the West African monsoon and premonsoon seasons (JAS and MAM, respectively), and to a lesser extent over Southern Africa.

At the shorter length scale (CP4A’s native grid; Fig. 4, thin solid lines), chaotic variability is larger, and hence the fractional FSPDND significance for seasonal means is somewhat lower over East and West Africa. Scale dependence is more limited over Southern Africa where fine-scale daily rainfall is more homogeneous (evidenced by enhanced temporal correlation between neighboring pairs; not shown), due to larger-scale weather systems.

The FSPDND for the intensity of extreme rain events (dashed lines) is also notably affected by fine-scale topographic variability, with similar interregional and interseasonal sensitivity to that of seasonal mean rainfall, apart from more muted responses in the West African premonsoon season (MAM) and the Southern African spring (OND) and summer (DJF). Fractional significance is however lower than for seasonal mean rainfall, likely due at least in part to the reduced power of testing for extremes (Fig. A1a). An additional factor may be that the fine-scale detail of changes in extremes could be less collocated with topographic features, especially in regions where the most intense convective systems have substantial lifetimes and propagation distances. A final remark from Fig. 4 is that length scale sensitivity is often weaker for extremes than seasonal means, and we suggest that, for extremes, relatively larger FSPD magnitudes at the native grid-scale (section 4) may compensate for poorer sampling.

b. Coastal impacts

Figure 5 illustrates the impact of coastal features on fractional FSPDND significance. In this case, grid boxes are binned according to their proximity to lake or ocean coastlines, excluding grid boxes of notable topographic variability (section 2b).

Fig. 5.
Fig. 5.

Impact of distance from nearest coastline on the fraction of CP4A statistically significant fine-scale projection detail (fractional FSPDND significance; left-hand axis), at the 10% level, for seasonal mean rainfall (solid lines) or the 99th percentile of daily rainfall intensity (dashed lines), at the 3-grid-length scale, for lake (thick lines) or ocean (thin lines) coastlines. Horizontal lines show the estimated rejection rate under the null hypothesis (solid or dashed for seasonal or extreme rain, respectively). Coastal distance bin widths are 10 km, shading shows the number of ocean coastal grid boxes analyzed per bin (right-hand axis), and thick sandy brown line shows the number of lake coastal grid boxes analyzed per bin. Arid regions (climatology < 1 mm day−1) are excluded, and data are absent where there are too few eligible grid boxes to analyze.

Citation: Journal of Climate 36, 4; 10.1175/JCLI-D-22-0009.1

The impact of coastal discontinuities on surface forcing, and hence on FSPDND, is small, with less sensitivity of fractional significance to coastal proximity than to topographic variability, noting the shorter left-hand y axis in Fig. 5. Nevertheless, FSPDND of seasonal mean rainfall is likely field significant close to lake shores (thick solid black lines), with H0 rejection rates reaching 20%–25% at the lake shores of East Africa (all seasons), West Africa (pre- and postmonsoon seasons) and Southern Africa (austral spring and summer). East Africa is most populated with lakes (thick sandy brown line), and further decomposition (not shown) finds that the impact on fine-scale detail here derives from both its Great Lakes (Victoria, Tanganyika, and Malawi) and, to a lesser extent, its smaller lakes.

In contrast, distance from ocean coastlines has little detectable impact on significance rates for seasonal means (Fig. 5, thin solid lines), with the exception of a small impact on the West African postmonsoon season. We speculate that the greater influence of lakes is due to their effect on the anomalous behavior of more prevalent organized convective systems in the continental interior. Other effects may be a relatively larger impact of small lakes on continental heat and moisture fluxes, and perhaps on their interactions with nearby topographic variability not accounted for by our rudimentary exclusion of more mountainous grid boxes. A further factor may be that ocean coastlines around Africa often lack fine-scale complexity, with their primary effect on heat and moisture fluxes—and hence rainfall—being at larger spatial scales and shorter (subdaily) temporal scales, such as their impact of sea breezes (Finney et al. 2020).

For the intensity of extreme rain events, no coastal influence on FSPDND is detected in the absence of large topographic variability, from lakes or oceans.

Overall, lake coasts often impact the fine-scale detail of seasonal mean rainfall in the CP4A projection, but otherwise the influence of coastal complexity is mostly dominated by sampling noise and does not warrant further consideration for impacts analysis at daily time scales, at least in these short simulations.

c. Urban impacts

The impact of urbanization on fractional FSPDND significance is shown in Fig. 6. Similar to the analysis of coastal influences, grid boxes are binned by proximity, but in this case their distance is to the nearest 25-km-scale urban fraction exceeding 0.1. The difficulty here is that many urban settlements are close to lake or ocean coasts, conflating these potential influences on FSPDND. We attempt to address this by excluding urban grid boxes less than 50 km from any coastline (or in mountainous regions; see section 2b), noting that this approximately halves the quantity of data within 100 km of urban developments.

Fig. 6.
Fig. 6.

Impact of distance from nearest urban conurbation (smoothed urban fraction > 0.1) on the fraction of CP4A statistically significant fine-scale projection detail (fractional FSPDND significance; left-hand axis), at the 10% level, for seasonal mean rainfall (solid lines) or the 99th percentile of daily rainfall intensity (dashed lines), at the 3-grid-length scale. Horizontal lines show the estimated rejection rate under the null hypothesis (solid or dashed for seasonal or extreme rain, respectively). Shading and right-hand axis show the number of grid boxes analyzed per 10-km urban distance bin. Arid regions (climatology < 1 mm day−1) are excluded, and data are absent where there are too few eligible grid boxes to analyze.

Citation: Journal of Climate 36, 4; 10.1175/JCLI-D-22-0009.1

Noting these caveats, Fig. 6 shows minimal increase in fractional significance as one draws closer to urban conurbations, even in Southern Africa with its much larger sample of inland urban grid boxes. Occurrences of larger interbin variability coincide with low bin counts, suggesting enhanced sampling variability. Thus, we find no detectable impact of urban surfaces on FSPDND for either seasonal mean rainfall or the intensity of extreme events. Similar results are obtained if only lake coastal settlements are excluded, or if settlements are instead delineated at individual grid boxes with larger urban fractional thresholds (e.g., 0.5, so incorporating numerous smaller towns and cities), or if all grid boxes are instead binned by their local standard deviation of urban fraction (not shown). Some effects of urbanization on FSPD may of course become detectable with longer or multiple simulations (which might also allow better separation of urban and coastal effects), so our results are best framed as revealing that such impacts are substantially less than topographic effects in CP4A, and perhaps also less than coastal effects. Further research is now needed with other models to determine whether this is robust and physically plausible or sensitive to the parameterization of urban areas; in CP4A, a simple bulk representation is employed (Best 2005; Best et al. 2011). Nevertheless, for these CP4A simulations, we conclude that there is no evidence to warrant application of projected daily rainfall data at sub-25-km scales around urban settlements for the metrics considered here.

4. Magnitude of fine-scale projection detail

While statistical significance of FSPDND is useful, and noting that an understood physical link between surface heterogeneity and FSPD would be similarly useful, either is insufficient for establishing whether fine-scale detail might become apparent in impacts studies. The FSPD of rainfall must also be of large enough amplitude to generate fine-scale heterogeneity of impacts that are in turn large enough to affect stakeholder decisions. This depends on both the amplitude of FSPD itself and on the climate sensitivities of the application and its associated decisions. This section examines the first of these.

We define the magnitude of fine-scale projection detail, termed FSPDSD, as the local standard deviation of percentage projection anomalies (100% × ΔR = 100% × Future/Control) across the 25 (5 × 5) grid boxes centered on each grid box. This therefore encompasses the two length scales considered earlier, and it will become relevant to note that this includes fine-scale chaotic variability as well as surface forcing effects. Regions of statistically significant FSPDND are favored by excluding ∼25-km boxes with a central grid box that has less than two out of eight significantly different neighboring pairs using the more robust 3-grid-length data (so also excluding arid regions).

Figure 7 illustrates the topographic dependence of FSPDSD as scatter density plots for the three large African regions. The substantial spread in FSPDSD, seen even in the absence of fine-scale topographic variability (Fig. 7; x = 0), likely arises primarily from random weather and climate variability (noting that its amplitude also depends on local climate characteristics), although this spread may also include the effects of small downstream heterogeneities due to remote topographic features.

Fig. 7.
Fig. 7.

Amplitude of sub-25-km projection detail (FSPDSD) for seasonal mean rainfall, where FSPDND is locally statistically significant. Shading shows the 2D histogram of the frequency of grid boxes (on a logarithmic scale normalized for each panel) binned by topographic variability (x axis) and FSPDSD (y axis). Green lines show the median (solid) and spread (10th and 90th percentiles; dashed) of FSPDSD with respect to topographic variability. Arid regions (climatology < 1 mm day−1) are excluded, and DJF in West Africa has too few eligible grid boxes to analyze.

Citation: Journal of Climate 36, 4; 10.1175/JCLI-D-22-0009.1

Nevertheless, Fig. 7 also illustrates a trend toward larger FSPDSD with increasing topographic variability, especially over East Africa (upper row). Mechanistically, in hilly and mountainous terrain, FSPDSD is caused by heterogeneous interactions between climate change processes and local topography, with these depending on the altitude, shape, and orientation of topographic features, as well as on the regional climate. These effects increase the median FSPDSD magnitude, and in the most mountainous regions of East Africa this is 20%–40% greater than that due to sampling effects (the latter judged from the median at x = 0). Recalling that our FSPDSD metric is the standard deviation (SD) of neighboring grid box values of ΔR, an approximation for the range of grid-scale projection anomalies across a 25-km locale is 4 times this SD, that is, 80%–160% of the local climatology (if the data were Gaussian distributed, which they are not, then 4SD would represent a 95% confidence interval). This seems substantive enough to be likely relevant to impacts modelers and stakeholders interested in local differences in mountainous regions.

In West Africa (Fig. 7, central row), a similar impact of topographic variability on the range of fine-scale climate change is found in the premonsoon season (MAM). This contrasts with only small impact during the peak and postmonsoon seasons (JAS and OND, respectively) when the distribution of FSPDSD in mountainous regions is little different to that due to the random grid-scale variability found in flat regions, despite often being statistically significant in JAS (Fig. 4). The peak of the dry season (DJF; Fig. 2) is too arid to offer sufficient eligible grid boxes. In Southern Africa (Fig. 7, lower row), any topographic impact on FSPDSD is also minimal, due at least partly to its lower topographic heterogeneity and smaller proportion of statistically significant locales (Fig. 4).

Proximity to ocean coastlines and urban regions has no detectable impact on FSPDSD (not shown), commensurate with their lack of impact on statistical significance (sections 3b and 3c). Locales close to lake shores typically exhibit median FSPDSD 5%–15% higher than elsewhere for seasonal mean data (Fig. S1 in the online supplemental material), suggesting an approximate range of fine-scale changes at sub-25-km scales of around a third (4 SD) of the local climatology along Africa’s lakes.

Last, Fig. S2 suggests that over East Africa the impact of topographic variability is often larger on FSPDSD of the intensity of extreme rain events than on that of seasonal means (even though statistical significance of FSPDND is more prevalent for seasonal means). This may reflect the larger impact of random sampling variability on the median and spread of the distribution of FSPDSD for extremes (seen at x = 0), which could shift the distribution to greater FSPDSD estimates in all regions irrespective of topographic variability. Alternatively, or additionally, a physically more interesting explanation is that it may be due to greater heterogeneity in interactions between climate change processes and local topography at the tail of the rainfall distribution. Elsewhere over Africa, topographic impacts on FSPDSD for extreme rain events are discernible only in the West African premonsoon season.

5. Benefits of spatial aggregation

In this section we instead consider regions where there is no significant fine-scale projection detail (i.e., low topographic variability away from lake coasts; see section 3) and ask about the extent to which uncertainty in projection information can be reduced if local data are first aggregated to a ∼25-km scale (this being a spatial pooling for extremes; see below). Reducing uncertainties due to near-grid-scale chaotic variability is advantageous to users, for example to better estimate climate deltas used to drive impacts models (unless it is desirable to retain full spatiotemporal weather characteristics; e.g., Miller et al. 2022).

We compute uncertainty as the variance of a large sample of decadal climate projection anomalies, and compare calculations between the grid scale and 25-km scale. Ideally, this would utilize a large initial condition ensemble of CP projections. However, this is currently impractical for Africa given the high cost of such simulations, so instead we compute the variance of projection anomalies across 1000 bootstrap resamples of the decadal climate metrics (following section 2d). A weakness of this approach is that lack of independence between bootstrap resamples causes an underestimate of the true sampling variability of decadal metrics. On the other hand, analysis of synthetic rainfall data demonstrates that this bias is approximately invariant to spatial scale and so does not concern the scale comparison here (more specifically, an extension of the conceptual model using 1000 independent simulations of 25 partially correlated grid boxes shows that a bootstrap-based estimate of the scale-sensitivity metric used below is biased less than 2% for seasonal means, and less than 10% for extremes; i.e., no substantial bias).

To focus on locales without significant FSPD, we analyze only grid boxes with less than two out of eight significant FSPDND (using the more robust 3-grid-length data, and noting a lack of sensitivity to the “two out of eight” threshold). Aggregated metrics are computed by first concatenating grid-scale Control and Future data over rolling 5 × 5 grid boxes before recomputing seasonal means or intensity of extremes at this 25-km scale for each of the 1000 bootstrap resamples (with each bootstrap resampling the same years for all grid boxes). This concatenation ensures enhanced temporal sampling of grid-scale rainfall intensities, but that results are not affected by the spatial-scale-sensitivity of the rainfall intensity distribution (Berthou et al. 2019b). Projection anomalies of Pseas and P99 are then computed as ΔS = Future − Control, so that their variance is not unduly affected by occasional large random ratios, and because we do not expect substantive fine-scale climatological heterogeneity in regions of insignificant surface forcing.

Figures 8a and 8b show examples, for OND, of the impact of spatial aggregation measured by the ratio of aggregated-to-raw variances of ΔSPseas or ΔSP99 [the variance ratio (VR)]. Uncertainties due to random weather variability are reduced by up to 50% for seasonal mean rainfall (locally exceeding this), and by up to 80% for the intensity of extreme events. This larger impact on extremes is expected, given the smaller data sample contributing to their calculation. The first-order pattern of variance reduction is latitudinal, exhibiting an equatorial peak with smaller reductions over Southern Africa and toward the Sahara. This is highlighted by Figs. 8c and 8d, showing aggregated-to-raw variance ratios against latitude, using concatenated metrics from all nonmissing seasons (conclusions for individual seasons are the same). We suggest this quasi-zonal stratification may be due to larger fractions of small-scale convective rainfall in the deep tropics, where substantive fine-scale heterogeneity leads to greater benefit from spatial aggregation than at subtropical latitudes where weather systems tend to be larger. However, even at any given latitude, the spread in uncertainty reductions is substantial (the y-direction range in Figs. 8c,d), likely reflecting a mix of sampling imprecision in the estimation of uncertainty reduction, some tendency for larger reductions where climatological mean rainfall is larger (especially for rainfall extremes; not shown), and variations in local climate characteristics.

Fig. 8.
Fig. 8.

Impact of spatial aggregation in regions of insignificant fine-scale projection detail, plotted as the variance ratio (VR; Table 1) that measures aggregated-to-raw uncertainty due to sampling variability. (top) Maps of VR for an exemplar season (OND), for (a) seasonal mean rainfall (Pseas) and (b) the 99th percentile of daily rainfall intensity (P99), with ratios averaged to a 1° scale for plotting. (middle) 2D histograms of grid box frequency (on a linear scale normalized for each panel) binned by latitude (x axis) and VR (y axis), for (c) Pseas and (d) P99, incorporating sub-Saharan (south of 20°N) data from all four seasons, and with the green line showing the median VR at each latitude. (bottom) 2D histograms of grid box frequency (on a logarithmic scale normalized for each panel) binned by the grid-scale absolute projection anomaly (|ΔS|; x axis) and the standard deviation of ΔS scaled by their local absolute projection anomaly (y axis), for (e) Pseas and (f) P99, incorporating sub-Saharan data from all four seasons, and with the green line showing median y values for each x-axis bin.

Citation: Journal of Climate 36, 4; 10.1175/JCLI-D-22-0009.1

Last, we evaluate the magnitude of these uncertainties against their local projection anomalies (ΔS). It is only if this uncertainty is substantive relative to ΔS that we can claim a reduction from spatial aggregation is potentially useful (with the extent of these benefits being application dependent). Figures 8e and 8f show the scatter density of the standard deviation (across bootstraps) of grid-scale ΔS relative to local absolute ΔS (i.e., sampling uncertainty scaled by |ΔS|) against the local absolute ΔS itself. Where projection anomalies are close to zero, the y-axis ratios inevitably tend to infinity, and are not meaningful. Elsewhere, the median of scaled sampling uncertainty (green line) is around a third. Since this is a scaled SD metric, multiplication by 4 infers an ∼95% confidence range of neighborhood grid-scale projection anomalies due to chaotic variability, which is thus typically similar in magnitude to the projection anomaly itself. Note that for less extreme scenarios than RCP8.5, or for nearer-term projection, sampling uncertainty relative to ΔS will be larger still.

In summary, in regions of insignificant FSPDND, aggregation of CP4A data to 25-km scales yields a potentially useful reduction in uncertainty across much of tropical sub-Saharan Africa for projections of seasonal mean rainfall and especially for projections of rainfall extremes.

6. Conclusions and discussion

Convection-permitting (CP) models offer the hope of better tailored climate projection information, particularly the dual promise of improved representation of convective rainfall events (including upscale effects to regional and planetary change) and of greater finesse in the detail of local climate change information. Both are crucial for decision-makers who need better understanding of the sensitivity of today’s decisions to plausible climate futures (e.g., Mittal et al. 2021; Orr et al. 2021; Miller et al. 2022). However, the reality of numerical modeling is that there is a gap between a model’s computational resolution and its effective resolution (e.g., Klaver et al. 2020), with the consequence that grid-scale rainfall events can be too intense at too small scales (e.g., Berthou et al. 2019b). This raises questions about whether and where it is beneficial to spatially aggregate CP model data. At locations where fine-scale heterogeneities are largely random and unforced, such aggregation brings the advantage of improved statistical sampling. Conversely, in other regions, avoiding (or limiting) aggregation can retain the influence of strong surface heterogeneities on local climate change, enabling the provision of the more localized information demanded by users, despite some bias in the distribution of rainfall intensities. Here we address these questions with a focus on the geolocated fine-scale projection detail (FSPD) of seasonal mean rainfall and the intensity of daily rainfall extremes, for a pair of 10-yr simulations for the vulnerable and varied continent of Africa, using a carefully considered statistical testing. We believe these methodologies can also be applied more broadly, and we speculate that (subject to confirmatory studies) many conclusions will be similar for other regions, while also noting that the threshold for FSPD detection (and so the desirability for spatial aggregation) is dependent on run length and ensemble size.

We find that, at sub-25-km scales, it is topographic variability that most commonly induces statistically significant FSPD, for both seasonal means and rainfall extremes. This is clearly evident in East Africa throughout the annual cycle, West Africa with seasonal dependence, and to a lesser extent over Southern Africa. Lake coastal features can also lead to statistically significant FSPD for seasonal means, and again with seasonal and regional dependence. Ocean coastlines and urban conurbations have little detectable impact on the projection detail of seasonal means or daily extremes in CP4A, although this does not rule out impacts on higher-frequency statistics, for example storms in specific circumstances or subdaily processes such as sea-breeze effects.

The magnitude of this fine-scale detail in CP4A’s projection (defined as typical grid box differences at sub-25-km scales, beyond that expected by chance) can be of similar magnitude to the local climatology in East Africa’s mountainous regions (all seasons) and West Africa’s mountains (boreal spring). The relative magnitude of the influence of coastal fine-scale detail along East Africa’s lakes may be around a third of this. Thus, for mountainous regions in particular, this local detail in climate change projections seems sufficiently substantive to be relevant to impacts modelers and stakeholders.

In flatter regions, distant from coastal and urban influences, fine-scale spatial heterogeneities in projected change are not significantly distinct from random variability. In this case, data aggregation to ∼25-km scales reduces the random component of variance, an effect seen most strongly in equatorial regions. This variance reduction can exceed 50% for seasonal mean rainfall in CP4A, and exceed 80% for the intensity of extreme events, although with substantial regional spread. Also, the typical range of neighboring grid-scale projection anomalies is similar to the projection anomaly itself, further demonstrating clear benefits of spatial aggregation of CP4A data. We therefore recommend such data aggregation for user applications in these regions unless retention of the full spatiotemporal variability of weather characteristics is required (in which case bias correction of the rainfall intensity distribution may be necessary).

This study has examined the extent, circumstances, and magnitude of geolocated fine-scale projection detail for a single CP model and a single continental region. The robustness of our conclusions, and their broader application, should now be confirmed or refuted by extending this approach to other models and regions. Additional research could also examine other variables. For example, one might ask whether urban boundaries have greater impact on the spatial detail of projected temperature change than on daily rainfall. Further study could also examine a range of spatial scales, perhaps taking a fluid approach toward determining the most appropriate aggregation scale for any given region, surface type, or variable. In some cases, the most appropriate scale for robust local impacts assessment may be substantially larger than that typically used in stakeholder-focused studies, due to the consequential reduction of substantial chaotic spatial variability. Another informative research avenue could be analysis of the role of aggregation in assessing temporal characteristics of subdaily data, in particular future changes in the duration and intensity behavior of storms, likely better captured by CP models’ improved representation of storm morphology, and with important implications for flooding. Last, in the long-term, as computational capacity further increases, and longer runs become possible, so local case studies of FSPD will become feasible. These would enable analysis and understanding of the heterogeneity of interactions between climate change processes and surface features, and thus a physically based evaluation of the extent to which fine-scale detail in climate projections is trustworthy.

Acknowledgments.

Funding was provided by the Met Office Weather and Climate Science for Service Partnership (WCSSP) South Africa project as part of the Newton Fund (DPR), the U.K. Foreign, Commonwealth and Development Office and Natural Environment Research Council’s joint Future Climate for Africa (FCFA) programme under the IMPALA project grant NE/M017265/1 (DPR), and by the Horizon 2020 project European Climate Prediction System (EUCP) grant agreement 776613 (SB). We are also very grateful to Rachel Stratton and Simon Tucker for running the CP4A experiments, to Steven Chan, John Marsham, and Elizabeth Kendon for useful discussions, and Francis Zwiers for a helpful peer review.

Data availability statement.

The CP4A dataset generated under the FCFA IMPALA project is publicly available, with currently a limited set of monthly mean variables downloadable from the Centre for Environmental Data Analysis (CEDA) archive (http://archive.ceda.ac.uk/; search for CP4A).

APPENDIX

Bias and Power of Significance Testing

Section 2d describes our approach toward addressing the first research question, namely testing the statistical significance of a null hypothesis (H0) of zero fine-scale projection detail, measured by differences between neighboring (near-)grid-scale projection anomalies, FSPDND. These statistical tests must be both powerful and unbiased, especially as bias in the rejection rate of H0 has the potential to confound our interpretation of FSPD. Alternatively, bias should at least be quantifiable, so that field significance can be estimated by comparing H0 rejection rates using climate model data with an expected H0 rejection rate. In particular, such bias may be affected by the short duration of the CP4A simulations. This appendix examines these issues by formulating a conceptual model to provide synthetic daily rainfall data, then employing those data to assess test bias and power under a range of parameter settings.

The conceptual model for daily rainfall R at either of two adjacent grid boxes, x = A or B, is as follows:
RxDay=(Climx×Anthrox)×[αInterannxSeason×NoisexDay×WDxDay(β)],
where Clim is the Control climatology for a given location and season; Anthro is a multiplicative factor that determines the left-hand bracketed term to be the Future climatology (so for a given large ensemble of simulations, the mean of right-hand bracketed term is scaled to unity, to force the average of all data in that ensemble to equal these Control and Future climatologies); Interann is a Gaussian distribution of ratios, transformed to be symmetric about unity (e.g., 0.5 transforms to 0.667, so as to have the same likelihood as 1.5), with one datum per year acting as a multiplicative factor on all 90 days of a season, scalable in amplitude by α, and identical between Control and Future; Noise is a gamma distribution of daily rainfall data, independent between Control and Future; and WD is a random binary array of wet and dry days (zeroes and ones) with climatological fraction β wet days. Note that since we compute only means and percentiles, no serial dependence is required. The spatial covariance (i.e., temporal correlation between A and B) of Interann, Noise, and WD is adjustable by specifying each as the sum of common and independent components.

For any given parameter set, 10 000 simulations are produced, each of 10 years × 90 days. Each ensemble of 10 000 simulations, and its corresponding parameter set, is referred to as an experiment. Typically, one parameter is varied across a suite of 11 experiments. The parameters and their defaults are as follows. Clim is 4 and 2 mm day−1 for A and B, respectively (this being an arbitrary differential to which no sensitivity is expected by design since ΔR is a ratio calculation), reflecting the sub-Saharan (south of 20°N) land-only CP4A climatology of 3 mm day−1. The default increase in Future rainfall is 20% for both A and B (AnthroA,B = 1.2; i.e., zero FSPDND). The default magnitude of Interann is α = 0.1, with no independent component between A and B. Other default parameter values are estimated from the medians of sub-Saharan land-only nonarid CP4A data: 0.44 and 0.47 are the shapes of the Control and Future gamma distributions, respectively; β = 0.90 and 0.84 are the Control and Future wet-day fractions, respectively; and 0.69 is the A-to-B correlation of Noise.

Each experiment of synthetic data provides 10 000 opportunities to test H0, namely that grid boxes A and B have zero difference between their population ΔR at the 10% significance level. Parametric and bootstrap tests are applied to each synthetic simulation (as per the CP4A data; section 2d), and thus a rejection rate for H0 is computed for each test across the 10 000 simulations. If AnthroA = AnthroB is specified for the population (i.e., H0 is valid), then an unbiased test should reject H0 on 10% of occasions at the nominal 10% level.

Figure A1a assesses the power and bias of the significance testing of FSPDND across 11 experiments with increasingly spatially distinct Anthro components. For the first experiment, x = 0, a spatially invariant 10% increase is applied (AnthroA,B = 1.1). Subsequent experiments then increase Anthro incrementally by 0.1 and 0.02 for A and B, respectively, so that the last experiment more than doubles the climatological Control rainfall at box A (AnthroA = 2.1), but increases the climatology by only 30% at box B (AnthroB = 1.3). Subjectively, this might be thought of as substantial FSPD.

For seasonal means, the parametric paired-difference test behaves well, with a 10% rejection rate at the 10% level for data satisfying H0 (Fig. A1a blue line at x = 0); this is expected, given the well-documented efficacy of the test, and that—in wet regions, at least—its assumptions are broadly valid for seasonal means. In comparison, the bootstrap approach rejects H0 too easily (Fig. A1a, thin solid brown line at x = 0), namely 15% of occasions at the nominal 10% significance level. Similar rejection rates were also found when applying this test to CP4A data in regions of homogeneous surface forcing (not shown), suggesting that this bias is not merely an artifact of the conceptual model. This bias arises because in a sample of only 10 years, a 10% tail is typically represented by just one year, but that year is omitted from more than 10% of bootstrap resamples (because many resamples omit at least two years, but very few omit none). Thus, the tail of the interannual distribution is underrepresented by the resamples, so the distribution of resampled seasonal climatologies is too narrow, and H0 is too easily rejected. Note that our short simulation length contributes to this bootstrap test bias, and that in longer simulations the tails are better represented, so test bias is reduced (e.g., for 50 years, the H0 rejection rate is 11%).

Fig. A1.
Fig. A1.

Rejection rates of a null hypothesis of no fine-scale projection detail, applied to synthetic rainfall data, and using bootstrapping (brown lines) and paired-difference (blue lines) tests. Rainfall metrics are seasonal means (solid lines) and the 99th percentile of daily rainfall intensity (dashed lines), derived from 10 years of data [or in (b), also 20 and 50 years]. Sensitivity is shown to (x axis): (a) differential anthropogenic forcing, (b) differential anthropogenic forcing and length of simulation (10, 20, 50 years, with decreasing line thickness, and no bootstrap test on seasonal means), (c) wet-day fraction (β) varied simultaneously in the Control and Future, (d) the ratio of Future-to-Control wet-day fraction, (e) the shape of the gamma distribution varied simultaneously in the Control and Future, (f) the ratio of Future-to-Control shape of the gamma distribution, (g) the ratio of B-to-A climatology, (h) the correlation of Noise between A and B varied simultaneously in the Control and Future (note that the x axis plots the correlation of full data, not Noise only), (i) the magnitude of Interann (α), and (j) the correlation of Interann between A and B.

Citation: Journal of Climate 36, 4; 10.1175/JCLI-D-22-0009.1

For the intensity of extreme events, only the bootstrap approach is assessed due to stronger skewness invalidating the Gaussian assumption required for parametric testing (following section 2d). For this metric, significance testing of FSPDND is marginally conservative, typically depicting a rejection rate of 9% under H0, rather than the expected 10% false positives (Fig. A1a, dashed brown line at x = 0).

As population FSPDND is then gradually amplified (x > 0; Fig. A1a); all testing rapidly detects more frequent statistically significant FSPDND. The power of the testing is less for extreme events than for seasonal means, due to the strong role of a small portion of daily data in determining the intensity of extremes, so analysis is subject to greater sampling noise. We also note that for seasonal means, the bootstrap test bias is consistent across a wide range of anthropogenic forcing (x values), suggesting that at least the regional patterns of climate model rejection rates would be relatively unbiased (only its overall rejection rate for short simulations).

Figures A1c–j illustrate the sensitivity of test bias to the parameters of the conceptual model, which can be interpreted as test sensitivity to large-scale patterns in CP4A climate characteristics. For seasonal means, the parametric test remains robust to substantial variations in all climate characteristics assessed, with the exception of aridity (low wet-day fraction or extreme low shape of the gamma distribution) where it is too conservative due to invalidity of the Gaussian assumption. Similarly, bootstrapping is robust to a diversity of climates (i.e., its bias is mostly invariant), again with the exception of arid environments [noting that biases are further enhanced with simultaneous multiple arid-appropriate parameter settings (not shown) and that repeated seasons of zero rainfall contribute a further source of bias in the most extreme locations]. Thus, we conclude that the parametric test outperforms the bootstrap test across a wide range of climates, so for the short simulations available here, this is our preferred choice for assessing FSPDND of seasonal means.

For the intensity of extremes, Figs. A1c–j show the bootstrap testing to be broadly robust to varying climate characteristics. Exceptions are again arid environments where test bias can be substantial in either direction (due to low wet-day fraction or extreme low shape of the gamma distribution), as well as some climatological sensitivity and bias in rejection rates with regard to neighborhood covariance of daily rain amounts.

The impact of hypothetically longer CP4A simulations is further examined in Fig. A1b, showing a substantial increase in the power of both the parametric and bootstrap tests as climate model simulation length increases (applied to seasonal means and extremes, respectively, and noting the shorter x-axis scale compared to Fig. A1a). For example, if we consider that FSPD becomes relevant if H0 is rejected at more than 50% of points in a given locality, then for seasonal means, CP simulations with durations of 10, 20, and 50 years can detect values of AnthroA − AnthroB = 0.10, 0.07, 0.04, respectively (i.e., more than halving the detectable FSPDND by this measure). For the intensity of extreme rain events, 10-, 20-, and 50-yr CP simulations can detect AnthroA − AnthroB = 0.25, 0.17, and 0.10, respectively.

Last, as a further aside, our conceptual model can also assess the power and sensitivity of previous applications of the bootstrapping approach to CP data (i.e., analysis of the statistical significance of projection anomalies or model-observed differences at single points; e.g., Berthou et al. 2019a; Kendon et al. 2019; Chan et al. 2020). In this case, subtractive anomalies are used (i.e., ΔS = Future − Control or ΔS = Model − Observed), only grid box A is analyzed (no neighborhood differences are computed), the default Clim is 3 mm day−1, and the default change in Future rainfall is zero (AnthroA = 1). Figure S3 shows that for seasonal means under default parameter settings, the bootstrap test again rejects H0 too easily (15% of occasions at the nominal 10% level), with a now similar bias for extremes (also a 15% rejection rate under H0). Bias is again broadly robust to the magnitude of anthropogenic forcing (or model simulation error), as well as to climatological patterns, except in arid locations with low gamma shape.

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  • Finney, D. L., J. H. Marsham, D. P. Rowell, E. J. Kendon, S. O. Tucker, R. A. Stratton, and L. S. Jackson, 2020: Effects of explicit convection on future projections of mesoscale circulations, rainfall, and rainfall extremes over eastern Africa. J. Climate, 33, 27012718, https://doi.org/10.1175/JCLI-D-19-0328.1.

    • Search Google Scholar
    • Export Citation
  • Fitzpatrick, R. G. J., and Coauthors, 2020: What drives the intensification of mesoscale convective systems over the West African Sahel under climate change? J. Climate, 33, 31533172, https://doi.org/10.1175/JCLI-D-19-0380.1.

    • Search Google Scholar
    • Export Citation
  • Fumière, Q., M. Déqué, O. Nuissier, S. Somot, A. Alias, C. Caillaud, O. Laurantin, and Y. Seity, 2020: Extreme rainfall in Mediterranean France during the fall: Added value of the CNRM-AROME convection-permitting regional climate model. Climate Dyn., 55, 7791, https://doi.org/10.1007/s00382-019-04898-8.

    • Search Google Scholar
    • Export Citation
  • Hart, N., R. Washington, and R. Stratton, 2018: Stronger local overturning in convective-permitting regional climate model improves simulation of the subtropical annual cycle. Geophys. Res. Lett., 45, 112334112342, https://doi.org/10.1029/2018GL079563.

    • Search Google Scholar
    • Export Citation
  • Hartley, A. J., N. MacBean, G. Georgievski, and S. Bontemps, 2017: Uncertainty in plant functional type distributions and its impact on land surface models. Remote Sens. Environ., 203, 7189, https://doi.org/10.1016/j.rse.2017.07.037.

    • Search Google Scholar
    • Export Citation
  • Hastings, D. A., and Coauthors, 1999: The Global Land One-Kilometer Base Elevation (GLOBE) digital elevation model, version 1.0. NOAA National Geophysical Data Center, accessed 23 July 2021, https://www.ngdc.noaa.gov/mgg/topo/globe.html.

  • Hook, S., R. C. Wilson, S. MacCallum, and C. J. Merchant, 2012: Global climate lake surface temperature [in “State of the Climate in 2011”]. Bull. Amer. Meteor. Soc., 93, S18S19, https://doi.org/10.1175/2012BAMSStateoftheClimate.1.

    • Search Google Scholar
    • Export Citation
  • Jackson, L. S., D. Finney, E. Kendon, J. Marsham, D. Parker, R. Stratton, L. Tomassini, and S. Tucker, 2020: The effect of explicit convection on couplings between rainfall, humidity and ascent over Africa under climate change. J. Climate, 33, 83158337, https://doi.org/10.1175/JCLI-D-19-0322.1.

    • Search Google Scholar
    • Export Citation
  • Jackson, L. S., J. H. Marsham, D. J. Parker, D. L. Finney, R. G. J. Fitzpatrick, D. P. Rowell, R. A. Stratton, and S. Tucker, 2022: The effect of explicit convection on climate change in the West African monsoon and central West African Sahel rainfall. J. Climate, 35, 15371557, https://doi.org/10.1175/JCLI-D-21-0258.1.

    • Search Google Scholar
    • Export Citation
  • Kendon, E. J., R. A. Stratton, S. Tucker, J. H. Marsham, S. Berthou, D. P. Rowell, and C. A. Senior, 2019: Enhanced future changes in wet and dry extremes over Africa at convection-permitting scale. Nat. Commun., 10, 1794, https://doi.org/10.1038/s41467-019-09776-9.

    • Search Google Scholar
    • Export Citation
  • Kendon, E. J., A. F. Prein, C. A. Senior, and A. Stirling, 2021: Challenges and outlook for convection-permitting climate modelling. Philos. Trans. Roy. Soc., A379, 20190547, https://doi.org/10.1098/rsta.2019.0547.

    • Search Google Scholar
    • Export Citation
  • Klaver, R., R. Haarsma, P. L. Vidale, and W. Hazeleger, 2020: Effective resolution in high resolution global atmospheric models for climate studies. Atmos. Sci. Lett., 21, e952, https://doi.org/10.1002/asl.952.

    • Search Google Scholar
    • Export Citation
  • Lucas-Picher, P., D. Argüeso, E. Brisson, Y. Tramblay, P. Berg, A. Lemonsu, S. Kotlarski, and C. Caillaud, 2021: Convection-permitting modeling with regional climate models: Latest developments and next steps. Wiley Interdiscip. Rev.: Climate Change, 12, e731, https://doi.org/10.1002/wcc.731.

    • Search Google Scholar
    • Export Citation
  • Miller, J., and Coauthors, 2022: A modelling-chain linking climate science and decision-makers for future urban flood management in West Africa. Reg. Environ. Change, 22, 93, https://doi.org/10.1007/s10113-022-01943-x.

    • Search Google Scholar
    • Export Citation
  • Mittal, N., and Coauthors, 2021: Tailored climate projections to assess site-specific vulnerability of tea production. Climate Risk Manage., 34, 100367, https://doi.org/10.1016/j.crm.2021.100367.

    • Search Google Scholar
    • Export Citation
  • Nicholson, S. E., 2018: Climate of the Sahel and West Africa. Oxford Research Encyclopedia of Climate Science, https://doi.org/10.1093/acrefore/9780190228620.013.510.

  • Orr, H. G., M. Ekström, M. B. Charlton, K. L. Peat, and H. J. Fowler, 2021: Using high-resolution climate change information in water management: A decision-makers’ perspective. Philos. Trans. Roy. Soc., 379A, 20200219, https://doi.org/10.1098/rsta.2020.0219.

    • Search Google Scholar
    • Export Citation
  • Pielke, R. A., 1991: A recommended specific definition of “resolution.” Bull. Amer. Meteor. Soc., 72, 1914, https://doi.org/10.1175/1520-0477-72.12.1914.

    • Search Google Scholar
    • Export Citation
  • Poujol, B., A. F. Prein, and A. J. Newman, 2020: Kilometer-scale modeling projects a tripling of Alaskan convective storms in future climate. Climate Dyn., 55, 35433564, https://doi.org/10.1007/s00382-020-05466-1.

    • Search Google Scholar
    • Export Citation
  • Poujol, B., P. A. Mooney, and S. P. Sobolowski, 2021: Physical processes driving intensification of future precipitation in the mid- to high latitudes. Environ. Res. Lett., 16, 34051, https://doi.org/10.1088/1748-9326/abdd5b.

    • Search Google Scholar
    • Export Citation
  • Poulter, B., and Coauthors, 2015: Plant functional type classification for Earth system models: Results from the European Space Agency’s land cover climate change initiative. Geosci. Model Dev., 8, 23152328, https://doi.org/10.5194/gmd-8-2315-2015.

    • Search Google Scholar
    • Export Citation
  • Prein, A. F., and Coauthors, 2015: A review on regional convection-permitting climate modeling: Demonstrations, prospects, and challenges. Rev. Geophys., 53, 323361, https://doi.org/10.1002/2014RG000475.

    • Search Google Scholar
    • Export Citation
  • Prein, A. F., C. Liu, K. Ikeda, S. B. Trier, R. M. Rasmussen, G. J. Holland, and M. P. Clark, 2017: Increased rainfall volume from future convective storms in the US. Nat. Climate Change, 7, 880884, https://doi.org/10.1038/s41558-017-0007-7.

    • Search Google Scholar
    • Export Citation
  • Prein, A. F., C. Liu, K. Ikeda, R. Bullock, R. M. Rasmussen, G. J. Holland, and M. Clark, 2020: Simulating North American mesoscale convective systems with a convection-permitting climate model. Climate Dyn., 55, 95110, https://doi.org/10.1007/s00382-017-3993-2.

    • Search Google Scholar
    • Export Citation
  • Rasmussen, K. L., A. F. Prein, R. M. Rasmussen, K. Ikeda, and C. Liu, 2020: Changes in the convective population and thermodynamic environments in convection-permitting regional climate simulations over the United States. Climate Dyn., 55, 383408, https://doi.org/10.1007/s00382-017-4000-7.

    • Search Google Scholar
    • Export Citation
  • Reynolds, R. W., T. M. Smith, C. Liu, D. B. Chelton, K. S. Casey, and M. G. Schlax, 2007: Daily high-resolution blended analyses for sea surface temperature. J. Climate, 20, 54735496, https://doi.org/10.1175/2007JCLI1824.1.

    • Search Google Scholar
    • Export Citation
  • Rowell, D. P., B. B. B. Booth, S. E. Nicholson, and P. Good, 2015: Reconciling past and future rainfall trends over East Africa. J. Climate, 28, 97689788, https://doi.org/10.1175/JCLI-D-15-0140.1.

    • Search Google Scholar
    • Export Citation
  • Senior, C. A., and Coauthors, 2020: Technical guidelines for using CP4-Africa simulation data (version 1). Zenodo, https://doi.org/10.5281/zenodo.4316467.

  • Senior, C. A., and Coauthors, 2021: Convection permitting regional climate change simulations for understanding future climate and informing decision making in Africa. Bull. Amer. Meteor. Soc., 102, E1206E1223, https://doi.org/10.1175/BAMS-D-20-0020.1.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., 2004: Evaluating mesoscale NWP models using kinetic energy spectra. Mon. Wea. Rev., 132, 30193032, https://doi.org/10.1175/MWR2830.1.

    • Search Google Scholar
    • Export Citation
  • Stein, T. H. M., R. J. Hogan, K. E. Hanley, J. C. Nicol, H. W. Lean, R. S. Plant, P. A. Clark, and C. E. Halliwell, 2014: The three-dimensional morphology of simulated and observed convective storms over southern England. Mon. Wea. Rev., 142, 32643283, https://doi.org/10.1175/MWR-D-13-00372.1.

    • Search Google Scholar
    • Export Citation
  • Stratton, R. A., and Coauthors, 2018: A pan-African convection permitting regional climate simulation with the Met Office Unified Model: CP4-Africa. J. Climate, 31, 34853508, https://doi.org/10.1175/JCLI-D-17-0503.1.

    • Search Google Scholar
    • Export Citation
  • von Storch, H., and F. W. Zwiers, 1999: Statistical Analysis in Climate Research. Cambridge University Press, 484 pp.

  • Wainwright, C. M., J. H. Marsham, D. P. Rowell, D. L. Finney, and E. Black, 2021: Future changes in seasonality in eastern Africa from regional simulations with explicit and parametrised convection. J. Climate, 34, 13671385, https://doi.org/10.1175/JCLI-D-20-0450.1.

    • Search Google Scholar
    • Export Citation
  • Webster, S., A. R. Brown, D. R. Cameron, and C. P. Jones, 2003: Improvements to the representation of orography in the Met Office Unified Model. Quart. J. Roy. Meteor. Soc., 129, 19892010, https://doi.org/10.1256/qj.02.133.

    • Search Google Scholar
    • Export Citation

Supplementary Materials

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  • Ban, N., and Coauthors, 2021: The first multi-model ensemble of regional climate simulations at kilometer-scale resolution, part I: Evaluation of precipitation. Climate Dyn., 57, 275302, https://doi.org/10.1007/s00382-021-05708-w.

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  • Berthou, S., E. J. Kendon, M. Roberts, D. P. Rowell, S. Tucker, and R. Stratton, 2019a: Larger future intensification of rainfall in West Africa in a convection-permitting model. Geophys. Res. Lett., 46, 132299132307, https://doi.org/10.1029/2019GL083544.

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  • Berthou, S., D. P. Rowell, E. J. Kendon, M. J. Roberts, R. Stratton, J. Crook, and C. Wilcox, 2019b: Improved climatological precipitation characteristics over West Africa at convection-permitting scales. Climate Dyn., 53, 19912011, https://doi.org/10.1007/s00382-019-04759-4.

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  • Chan, S. C., E. J. Kendon, S. Berthou, G. Fosser, E. Lewis, and H. J. Fowler, 2020: Europe-wide precipitation projections at convection permitting scale with the Unified Model. Climate Dyn., 55, 409428, https://doi.org/10.1007/s00382-020-05192-8.

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  • Crook, J., C. Klein, S. Folwell, C. M. Taylor, D. J. Parker, and T. Stein, 2019: Assessment of the representation of West African storm lifecycles in convection-permitting simulations. Earth Space Sci., 6, 818835, https://doi.org/10.1029/2018EA000491.

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  • Dai, A., R. M. Rasmussen, C. Liu, K. Ikeda, and A. F. Prein, 2020: A new mechanism for warm-season precipitation response to global warming based on convection-permitting simulations. Climate Dyn., 55, 343368, https://doi.org/10.1007/s00382-017-3787-6.

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  • Finney, D. L., and Coauthors, 2019: Implications of improved representation of convection for the East Africa water budget using a convection-permitting model. J. Climate, 32, 21092129, https://doi.org/10.1175/JCLI-D-18-0387.1.

    • Search Google Scholar
    • Export Citation
  • Finney, D. L., J. H. Marsham, D. P. Rowell, E. J. Kendon, S. O. Tucker, R. A. Stratton, and L. S. Jackson, 2020: Effects of explicit convection on future projections of mesoscale circulations, rainfall, and rainfall extremes over eastern Africa. J. Climate, 33, 27012718, https://doi.org/10.1175/JCLI-D-19-0328.1.

    • Search Google Scholar
    • Export Citation
  • Fitzpatrick, R. G. J., and Coauthors, 2020: What drives the intensification of mesoscale convective systems over the West African Sahel under climate change? J. Climate, 33, 31533172, https://doi.org/10.1175/JCLI-D-19-0380.1.

    • Search Google Scholar
    • Export Citation
  • Fumière, Q., M. Déqué, O. Nuissier, S. Somot, A. Alias, C. Caillaud, O. Laurantin, and Y. Seity, 2020: Extreme rainfall in Mediterranean France during the fall: Added value of the CNRM-AROME convection-permitting regional climate model. Climate Dyn., 55, 7791, https://doi.org/10.1007/s00382-019-04898-8.

    • Search Google Scholar
    • Export Citation
  • Hart, N., R. Washington, and R. Stratton, 2018: Stronger local overturning in convective-permitting regional climate model improves simulation of the subtropical annual cycle. Geophys. Res. Lett., 45, 112334112342, https://doi.org/10.1029/2018GL079563.

    • Search Google Scholar
    • Export Citation
  • Hartley, A. J., N. MacBean, G. Georgievski, and S. Bontemps, 2017: Uncertainty in plant functional type distributions and its impact on land surface models. Remote Sens. Environ., 203, 7189, https://doi.org/10.1016/j.rse.2017.07.037.

    • Search Google Scholar
    • Export Citation
  • Hastings, D. A., and Coauthors, 1999: The Global Land One-Kilometer Base Elevation (GLOBE) digital elevation model, version 1.0. NOAA National Geophysical Data Center, accessed 23 July 2021, https://www.ngdc.noaa.gov/mgg/topo/globe.html.

  • Hook, S., R. C. Wilson, S. MacCallum, and C. J. Merchant, 2012: Global climate lake surface temperature [in “State of the Climate in 2011”]. Bull. Amer. Meteor. Soc., 93, S18S19, https://doi.org/10.1175/2012BAMSStateoftheClimate.1.

    • Search Google Scholar
    • Export Citation
  • Jackson, L. S., D. Finney, E. Kendon, J. Marsham, D. Parker, R. Stratton, L. Tomassini, and S. Tucker, 2020: The effect of explicit convection on couplings between rainfall, humidity and ascent over Africa under climate change. J. Climate, 33, 83158337, https://doi.org/10.1175/JCLI-D-19-0322.1.

    • Search Google Scholar
    • Export Citation
  • Jackson, L. S., J. H. Marsham, D. J. Parker, D. L. Finney, R. G. J. Fitzpatrick, D. P. Rowell, R. A. Stratton, and S. Tucker, 2022: The effect of explicit convection on climate change in the West African monsoon and central West African Sahel rainfall. J. Climate, 35, 15371557, https://doi.org/10.1175/JCLI-D-21-0258.1.

    • Search Google Scholar
    • Export Citation
  • Kendon, E. J., R. A. Stratton, S. Tucker, J. H. Marsham, S. Berthou, D. P. Rowell, and C. A. Senior, 2019: Enhanced future changes in wet and dry extremes over Africa at convection-permitting scale. Nat. Commun., 10, 1794, https://doi.org/10.1038/s41467-019-09776-9.

    • Search Google Scholar
    • Export Citation
  • Kendon, E. J., A. F. Prein, C. A. Senior, and A. Stirling, 2021: Challenges and outlook for convection-permitting climate modelling. Philos. Trans. Roy. Soc., A379, 20190547, https://doi.org/10.1098/rsta.2019.0547.

    • Search Google Scholar
    • Export Citation
  • Klaver, R., R. Haarsma, P. L. Vidale, and W. Hazeleger, 2020: Effective resolution in high resolution global atmospheric models for climate studies. Atmos. Sci. Lett., 21, e952, https://doi.org/10.1002/asl.952.

    • Search Google Scholar
    • Export Citation
  • Lucas-Picher, P., D. Argüeso, E. Brisson, Y. Tramblay, P. Berg, A. Lemonsu, S. Kotlarski, and C. Caillaud, 2021: Convection-permitting modeling with regional climate models: Latest developments and next steps. Wiley Interdiscip. Rev.: Climate Change, 12, e731, https://doi.org/10.1002/wcc.731.

    • Search Google Scholar
    • Export Citation
  • Miller, J., and Coauthors, 2022: A modelling-chain linking climate science and decision-makers for future urban flood management in West Africa. Reg. Environ. Change, 22, 93, https://doi.org/10.1007/s10113-022-01943-x.

    • Search Google Scholar
    • Export Citation
  • Mittal, N., and Coauthors, 2021: Tailored climate projections to assess site-specific vulnerability of tea production. Climate Risk Manage., 34, 100367, https://doi.org/10.1016/j.crm.2021.100367.

    • Search Google Scholar
    • Export Citation
  • Nicholson, S. E., 2018: Climate of the Sahel and West Africa. Oxford Research Encyclopedia of Climate Science, https://doi.org/10.1093/acrefore/9780190228620.013.510.

  • Orr, H. G., M. Ekström, M. B. Charlton, K. L. Peat, and H. J. Fowler, 2021: Using high-resolution climate change information in water management: A decision-makers’ perspective. Philos. Trans. Roy. Soc., 379A, 20200219, https://doi.org/10.1098/rsta.2020.0219.

    • Search Google Scholar
    • Export Citation
  • Pielke, R. A., 1991: A recommended specific definition of “resolution.” Bull. Amer. Meteor. Soc., 72, 1914, https://doi.org/10.1175/1520-0477-72.12.1914.

    • Search Google Scholar
    • Export Citation
  • Poujol, B., A. F. Prein, and A. J. Newman, 2020: Kilometer-scale modeling projects a tripling of Alaskan convective storms in future climate. Climate Dyn., 55, 35433564, https://doi.org/10.1007/s00382-020-05466-1.

    • Search Google Scholar
    • Export Citation
  • Poujol, B., P. A. Mooney, and S. P. Sobolowski, 2021: Physical processes driving intensification of future precipitation in the mid- to high latitudes. Environ. Res. Lett., 16, 34051, https://doi.org/10.1088/1748-9326/abdd5b.

    • Search Google Scholar
    • Export Citation
  • Poulter, B., and Coauthors, 2015: Plant functional type classification for Earth system models: Results from the European Space Agency’s land cover climate change initiative. Geosci. Model Dev., 8, 23152328, https://doi.org/10.5194/gmd-8-2315-2015.

    • Search Google Scholar
    • Export Citation
  • Prein, A. F., and Coauthors, 2015: A review on regional convection-permitting climate modeling: Demonstrations, prospects, and challenges. Rev. Geophys., 53, 323361, https://doi.org/10.1002/2014RG000475.

    • Search Google Scholar
    • Export Citation
  • Prein, A. F., C. Liu, K. Ikeda, S. B. Trier, R. M. Rasmussen, G. J. Holland, and M. P. Clark, 2017: Increased rainfall volume from future convective storms in the US. Nat. Climate Change, 7, 880884, https://doi.org/10.1038/s41558-017-0007-7.

    • Search Google Scholar
    • Export Citation
  • Prein, A. F., C. Liu, K. Ikeda, R. Bullock, R. M. Rasmussen, G. J. Holland, and M. Clark, 2020: Simulating North American mesoscale convective systems with a convection-permitting climate model. Climate Dyn., 55, 95110, https://doi.org/10.1007/s00382-017-3993-2.

    • Search Google Scholar
    • Export Citation
  • Rasmussen, K. L., A. F. Prein, R. M. Rasmussen, K. Ikeda, and C. Liu, 2020: Changes in the convective population and thermodynamic environments in convection-permitting regional climate simulations over the United States. Climate Dyn., 55, 383408, https://doi.org/10.1007/s00382-017-4000-7.

    • Search Google Scholar
    • Export Citation
  • Reynolds, R. W., T. M. Smith, C. Liu, D. B. Chelton, K. S. Casey, and M. G. Schlax, 2007: Daily high-resolution blended analyses for sea surface temperature. J. Climate, 20, 54735496, https://doi.org/10.1175/2007JCLI1824.1.

    • Search Google Scholar
    • Export Citation
  • Rowell, D. P., B. B. B. Booth, S. E. Nicholson, and P. Good, 2015: Reconciling past and future rainfall trends over East Africa. J. Climate, 28, 97689788, https://doi.org/10.1175/JCLI-D-15-0140.1.

    • Search Google Scholar
    • Export Citation
  • Senior, C. A., and Coauthors, 2020: Technical guidelines for using CP4-Africa simulation data (version 1). Zenodo, https://doi.org/10.5281/zenodo.4316467.

  • Senior, C. A., and Coauthors, 2021: Convection permitting regional climate change simulations for understanding future climate and informing decision making in Africa. Bull. Amer. Meteor. Soc., 102, E1206E1223, https://doi.org/10.1175/BAMS-D-20-0020.1.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W. C., 2004: Evaluating mesoscale NWP models using kinetic energy spectra. Mon. Wea. Rev., 132, 30193032, https://doi.org/10.1175/MWR2830.1.

    • Search Google Scholar
    • Export Citation
  • Stein, T. H. M., R. J. Hogan, K. E. Hanley, J. C. Nicol, H. W. Lean, R. S. Plant, P. A. Clark, and C. E. Halliwell, 2014: The three-dimensional morphology of simulated and observed convective storms over southern England. Mon. Wea. Rev., 142, 32643283, https://doi.org/10.1175/MWR-D-13-00372.1.

    • Search Google Scholar
    • Export Citation
  • Stratton, R. A., and Coauthors, 2018: A pan-African convection permitting regional climate simulation with the Met Office Unified Model: CP4-Africa. J. Climate, 31, 34853508, https://doi.org/10.1175/JCLI-D-17-0503.1.

    • Search Google Scholar
    • Export Citation
  • von Storch, H., and F. W. Zwiers, 1999: Statistical Analysis in Climate Research. Cambridge University Press, 484 pp.

  • Wainwright, C. M., J. H. Marsham, D. P. Rowell, D. L. Finney, and E. Black, 2021: Future changes in seasonality in eastern Africa from regional simulations with explicit and parametrised convection. J. Climate, 34, 13671385, https://doi.org/10.1175/JCLI-D-20-0450.1.

    • Search Google Scholar
    • Export Citation
  • Webster, S., A. R. Brown, D. R. Cameron, and C. P. Jones, 2003: Improvements to the representation of orography in the Met Office Unified Model. Quart. J. Roy. Meteor. Soc., 129, 19892010, https://doi.org/10.1256/qj.02.133.

    • Search Google Scholar
    • Export Citation
  • Fig. 1.

    Maps of CP4A (a) topographic height (m), (b) local topographic standard deviation (m) (defined in section 2b and Table 1), and (c) distance from the nearest large urban conurbation (smoothed urban fraction > 0.1). All data are averaged to a 0.25° scale for plotting. Boxes show the three subcontinental regions.

  • Fig. 2.

    Maps of CP4A Control climatological rainfall (mm day−1), averaged over all years. Data are averaged to a 1° scale for plotting. Boxes show the three subcontinental regions.

  • Fig. 3.

    Maps of the fraction of CP4A statistically significant fine-scale projection detail (fractional FSPDND significance), at the 10% level, computed for each 1° box, for (left) seasonal mean rainfall and (right) the 99th percentile of daily rainfall intensity. The analysis uses data first smoothed to a 3-grid-length scale. The right-hand color scale is shifted to center on the 9% null hypothesis rejection rate found in the conceptual model (yellow). Arid regions (climatology < 1 mm day−1) vulnerable to significance bias are masked (white).

  • Fig. 4.

    Impact of topographic variability on the fraction of CP4A statistically significant fine-scale projection detail (fractional FSPDND significance; left-hand axis), at the 10% level, for seasonal mean rainfall (solid lines) or the 99th percentile of daily rainfall intensity (dashed lines), at the 3-grid-length scale (thick lines) or on the native grid (thin lines). Topographic variability bin sizes increase nonlinearly, with fractional significance plotted against the mean topographic variability of each bin. Horizontal lines show the estimated rejection rate under the null hypothesis (solid or dashed for seasonal or extreme rain, respectively). Shading (right-hand axis) shows analyzed grid box counts in evenly spaced 40-m topographic variability bins. Arid regions (climatology < 1 mm day−1) are excluded, and DJF in West Africa has too few eligible grid boxes to analyze.

  • Fig. 5.

    Impact of distance from nearest coastline on the fraction of CP4A statistically significant fine-scale projection detail (fractional FSPDND significance; left-hand axis), at the 10% level, for seasonal mean rainfall (solid lines) or the 99th percentile of daily rainfall intensity (dashed lines), at the 3-grid-length scale, for lake (thick lines) or ocean (thin lines) coastlines. Horizontal lines show the estimated rejection rate under the null hypothesis (solid or dashed for seasonal or extreme rain, respectively). Coastal distance bin widths are 10 km, shading shows the number of ocean coastal grid boxes analyzed per bin (right-hand axis), and thick sandy brown line shows the number of lake coastal grid boxes analyzed per bin. Arid regions (climatology < 1 mm day−1) are excluded, and data are absent where there are too few eligible grid boxes to analyze.

  • Fig. 6.

    Impact of distance from nearest urban conurbation (smoothed urban fraction > 0.1) on the fraction of CP4A statistically significant fine-scale projection detail (fractional FSPDND significance; left-hand axis), at the 10% level, for seasonal mean rainfall (solid lines) or the 99th percentile of daily rainfall intensity (dashed lines), at the 3-grid-length scale. Horizontal lines show the estimated rejection rate under the null hypothesis (solid or dashed for seasonal or extreme rain, respectively). Shading and right-hand axis show the number of grid boxes analyzed per 10-km urban distance bin. Arid regions (climatology < 1 mm day−1) are excluded, and data are absent where there are too few eligible grid boxes to analyze.

  • Fig. 7.

    Amplitude of sub-25-km projection detail (FSPDSD) for seasonal mean rainfall, where FSPDND is locally statistically significant. Shading shows the 2D histogram of the frequency of grid boxes (on a logarithmic scale normalized for each panel) binned by topographic variability (x axis) and FSPDSD (y axis). Green lines show the median (solid) and spread (10th and 90th percentiles; dashed) of FSPDSD with respect to topographic variability. Arid regions (climatology < 1 mm day−1) are excluded, and DJF in West Africa has too few eligible grid boxes to analyze.

  • Fig. 8.

    Impact of spatial aggregation in regions of insignificant fine-scale projection detail, plotted as the variance ratio (VR; Table 1) that measures aggregated-to-raw uncertainty due to sampling variability. (top) Maps of VR for an exemplar season (OND), for (a) seasonal mean rainfall (Pseas) and (b) the 99th percentile of daily rainfall intensity (P99), with ratios averaged to a 1° scale for plotting. (middle) 2D histograms of grid box frequency (on a linear scale normalized for each panel) binned by latitude (x axis) and VR (y axis), for (c) Pseas and (d) P99, incorporating sub-Saharan (south of 20°N) data from all four seasons, and with the green line showing the median VR at each latitude. (bottom) 2D histograms of grid box frequency (on a logarithmic scale normalized for each panel) binned by the grid-scale absolute projection anomaly (|ΔS|; x axis) and the standard deviation of ΔS scaled by their local absolute projection anomaly (y axis), for (e) Pseas and (f) P99, incorporating sub-Saharan data from all four seasons, and with the green line showing median y values for each x-axis bin.

  • Fig. A1.

    Rejection rates of a null hypothesis of no fine-scale projection detail, applied to synthetic rainfall data, and using bootstrapping (brown lines) and paired-difference (blue lines) tests. Rainfall metrics are seasonal means (solid lines) and the 99th percentile of daily rainfall intensity (dashed lines), derived from 10 years of data [or in (b), also 20 and 50 years]. Sensitivity is shown to (x axis): (a) differential anthropogenic forcing, (b) differential anthropogenic forcing and length of simulation (10, 20, 50 years, with decreasing line thickness, and no bootstrap test on seasonal means), (c) wet-day fraction (β) varied simultaneously in the Control and Future, (d) the ratio of Future-to-Control wet-day fraction, (e) the shape of the gamma distribution varied simultaneously in the Control and Future, (f) the ratio of Future-to-Control shape of the gamma distribution, (g) the ratio of B-to-A climatology, (h) the correlation of Noise between A and B varied simultaneously in the Control and Future (note that the x axis plots the correlation of full data, not Noise only), (i) the magnitude of Interann (α), and (j) the correlation of Interann between A and B.

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