# The April 2010 North African heatwave: when the water vapor greenhouse effect drives nighttime temperatures

Yann Largeron, Françoise Guichard, Romain Roehrig, Fleur Couvreux, Jessica Barbier

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Yann Largeron, Françoise Guichard, Romain Roehrig, Fleur Couvreux, Jessica Barbier. The April 2010 North African heatwave: when the water vapor greenhouse effect drives nighttime temperatures. Climate Dynamics, 2020, 54 (9-10), pp.3879-3905. 10.1007/s00382-020-05204-7. hal-04816378

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# The April 2010 North African heatwave: when the water vapor greenhouse effect drives nighttime temperatures

Yann Largeron · Françoise Guichard · Romain

Roehrig · Fleur Couvreux · Jessica Barbier

Received: date / Accepted: date

**Abstract** North Africa experienced a severe heatwave in April 2010 with daily maximum temperatures (*T*<sub>max</sub>) frequently exceeding 40°C and daily minimum temperatures (*T*<sub>min</sub>) over 27°C for more than five consecutive days in extended Saharan and Sahelian areas. Observations show that areas and periods affected by the heatwave correspond to strong positive anomalies of surface incoming longwave fluxes (*LW*<sub>in</sub>) and negative anomalies of incoming shortwave fluxes (*SW*<sub>in</sub>). The latter are explained by clouds in the Sahara, and by both clouds and dust loadings in the Sahel. However, the strong positive anomalies of *LW*<sub>in</sub> are hardly related to cloud or aerosol radiative effects.

An analysis based on climate-model simulations (CNRM-AM) complemented by a specially-designed conceptual soil-atmospheric surface layer model (SARAWI) shows that this positive anomaly of *LW*<sub>in</sub> is mainly due to a water vapor greenhouse effect. SARAWI, which represents the two processes driving temperatures, namely turbulence and longwave radiative transfer between the soil and the atmospheric surface layer, points to the crucial impact of synoptic low-level advection of water vapor on *T*<sub>min</sub>. By increasing the atmospheric infrared emissivity, the advected water vapor dramatically increases the nocturnal radiative warming of the soil surface, then in turn reducing the nocturnal cooling of the atmospheric surface layer, which remains warm throughout the night. Over Western Sahel, this advection is related to an early northward incursion of the monsoon flow. Over Sahara, the anomalously high precipitable water is due to a tropical plume event. Both observations and simulations support this major influence of the low-level water vapor radiative effect on *T*<sub>min</sub> during this spring heatwave.

**Keywords** Heatwave · Radiative physics · Greenhouse effect · North Africa
# 1 Introduction

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Heatwaves and their impacts over Europe or Western countries have been widely studied (e.g. [Beniston, 2004], [Black et al., 2004], [Perkins, 2015] for a review). They received much less attention elsewhere, especially in North Africa. However, climate projections indicate that North Africa, where climate is among the warmest and driest on Earth, will be particularly affected by climate changes in a near future [Roehrig et al., 2013; Deme et al., 2017]. Furthermore, heatwaves have become more frequent and severe in the past three decades [Fontaine et al., 2013; Moron et al., 2016] and these trends are projected to continue [IPCC, 2013]. This could become an exacerbating factor of vulnerability of North African societies whose adaptation strategies appear limited, due to their low hydrological resources and agricultural productivity [IPCC, 2014; Sultan and Gaetani, 2016].

In the Sahel, springtime has exhibited a strong trend of climate warming since 1950 [Guichard et al., 2012, 2017], up to twice the corresponding trend observed over Europe. This strong warming more significantly occurs during the hottest months of the year (April, May), at the end of the dry season, before the onset of the West African monsoon. This combination leads to heatwaves of unprecedented strong magnitude, an example of which occurred in spring 2010, where temperature peaks higher than $45^{\circ}C$ were recorded in many Sahelian countries (Niger, Senegal, Mali, Burkina Faso and Chad). These very high temperatures had strong impacts on morbidity and mortality (e.g. [Honda et al., 2014]).

Progressive multi-day soil desiccation has been recently pointed out as a major process operating during mid-latitude mega-heatwaves, like those who took place in Europe in 2003 or in Russia in 2010 ([Miralles et al., 2014; Fischer, 2014]). However, this process is unlikely to operate over North Africa during springtime since soils are mostly dry at this period of the year and remain so until the arrival of the monsoon rain (e.g. [Baup et al., 2007]). In contrast, Sahelian heatwaves appear to be frequently associated with an increase of moisture ([Guichard et al., 2009] and further evidences in the present study). Physical mechanisms operating during these heatwaves therefore still need to be identified.

Using in-situ observations in the central Sahel, Guichard et al. [2009] show that night-time minimum temperatures increase by several degrees during the first incursions of the moist monsoon flow in spring, while the incoming longwave flux at the surface varies accordingly. Therefore, couplings between surface air temperature, humidity and radiative fluxes are expected, particularly during nighttime. On the other hand, springtime in the Sahel is often associated with high dust loadings [Brooks and Legrand, 2000; Basart et al., 2009; Klose et al., 2010], mid-level clouds and cirrus. These processes are likely to limit daytime incoming fluxes, boundary layer growth and therefore daytime warming. These contrasting impacts on low-levels suggest a strong diurnal cycle of the physical processes acting during springtime heatwaves, implying reduced daytime warming and reduced nighttime cooling with partly compensating effects on daily-average temperatures in unknown proportions.

Over the Sahel and Sahara, the surface and Top Of Atmosphere (TOA) energy budget is affected by aerosols, that are known to have a radiative impact both in the longwave and shortwave band, generally leading to a negative net effect [Balkanski et al., 2007]. Similarly, cloud cover induce a longwave warming generally overcompensated by a shortwave cooling [Bouniol et al., 2012]. Recently, Marsham et al. [2016] studied the respective impacts of water vapor and dust aerosols in controlling the radiative budget over the Sahara, using both in-situ observations and satellite retrievals. They concluded that the total column water vapor provides a stronger control on TOA net radiative fluxes than the aerosols. However, they also noted that dust loadings are correlated to water vapor, so that their methodology can not disentangle the relative effect of each other.
Identifying the physical mechanisms at play in North Africa during springtime, and especially during heatwaves; describing their diurnal cycle evolution; their impact on the surface energy budget and the near surface temperature therefore still need to be done. The present study aims at filling these gaps, with a particular focus on the major heatwave of April 2010. In line with these objectives, we will also present a new approach making use of a specially-designed conceptual model that allows to isolate the radiative impact of water vapor alone and therefore directly quantify its impact on the energy budget, distinctly from the effects of aerosols and clouds.

This study shows that the 2010 heatwave is characterized by strong positive anomalies of the daily-minimum temperatures and the incoming longwave fluxes over North Africa by making use of several long-term observational datasets (satellite-based products and ground-stations, described in section 2). It further explores the radiative impacts of clouds and aerosols on 2m-temperatures (sections 3 and 4) and shows that, although strong positive anomalies of AOD and cloud cover are found respectively over the Sahel and Sahara, their radiative impacts are too weak to explain the anomalies of longwave fluxes and temperatures. Boundary-layer physics is further explored with climate simulations performed with the atmospheric component of the Centre National de Recherches Météorologiques (CNRM) climate model, using a configuration in which the dynamics is nudged towards a reanalysis (section 5). It shows that turbulence in the atmospheric surface layer and long-wave radiation are the main drivers of the evolution of 2m-temperatures during the heat-wave and that the longwave radiative coupling between the soil and the air surface layer is strongly affected by the infrared emissivity of the atmosphere, which is in turn strongly related to the 2m-specific humidity. Finally, a new and specially designed prognostic model of surface-atmosphere radiative exchanges (hereafter called SARAWI) is presented. This model is used to explore and quantify the impact of the radiative greenhouse effect of water vapor on surface air temperature (section 6), and we introduce a Humidity Radiative Effect (hereafter HRE) based on the model estimates. It shows that the heatwave is controlled by the anomalously high specific humidity related to an early monsoon flux intrusion into the Sahel, and to a coincident tropical plume into the Sahara. Conclusions are given in the final section.

# 2 Data and methods

## 2.1 Surface temperature databases

This study makes use of the Berkeley Earth Surface Temperature gridded dataset, hereafter referred to as BEST. This product uses the statistical Kriging method to interpolate data from ground-based stations on a global regular 1° × 1° grid [Rohde et al., 2013]. The dataset uses 2m-temperatures from an ensemble of weather stations compiled from 16 preexisting data archives, among which the Global Historical Climatology Network (GHCN), and further compiles data over 39000 ground-stations.

In the following, we use daily-minimum, daily-maximum and daily-average temperatures $T_{min}$, $T_{max}$ and $T_{avg}$ which are available from 1880 to 2013, at a daily time scale.

For each grid point, we compute daily climatological values over the 2000-2013 period (by averaging values for the 14 years and using a 21-days running-mean) for $T_{min}$, $T_{max}$ and $T_{avg}$. Hereafter, daily anomalies for 2010 are estimated from this 2000-2013 climatology (this relatively short period, 2000-2013, was chosen for consistency with the analysis of the satellite data presented below). We also compute, at each grid point, the daily 90% quantile
values of the temperature distributions built with the 21 × 14 = 294 values of the 21 calendar days centered on the considered day and the 14 years of the 2000-2013 period.

We also used data from 222 SYNOP ground stations across North Africa archived by the French weather service Météo-France.

## 2.2 The Clouds and the Earth's Radiant Energy System (CERES) database

We also use data from the Clouds and the Earth's Radiant Energy System (CERES) database, developed by NASA [Wielicki et al., 1996, 1998], which are available from 2000 to 2017. We use the SYN1DEG dataset, which is a level 3 satellite product which provides CERES-observed radiative fluxes at 3-hourly and daily temporal resolution on a 1° × 1° grid, together with coincident Moderate Resolution Imaging Spectroradiometer (MODIS)-derived cloud and aerosol properties, and geostationary-derived cloud properties and broadband fluxes that have been carefully normalized with CERES fluxes. The use of measurements from a constellation of geostationary orbiting satellites allows to more accurately model the variability between CERES Terra and Aqua satellite observations (cf [Doelling et al., 2013] for a description of the methodology). This dataset also provides daily average 1° × 1° grid-ded data of cloud cover, total Aerosol Optical Depth at 0.55 µm (hereafter AOD), and total column Precipitable Water (hereafter PW) estimated by MODIS.

We also use the Earth's surface computed upwelling and incoming shortwave (hereafter SW<sub>in</sub> and SW<sub>up</sub>) and longwave (LW<sub>in</sub> and LW<sub>up</sub>) fluxes, for all-sky, clear-sky (cloud free) and pristine (cloud and aerosol free, hereafter referred to as clean-sky) conditions. Surface fluxes are provided with a 3 h timestep using a radiative transfer code ([Fu and Liou, 1992]) based upon inputs from Terra and Aqua MODIS and 3-hourly geostationary data (for cloud and aerosol properties), and meteorological assimilation data from the Goddard Earth Observing System Model reanalyses (for meteorological profiles). Several sources of uncertainties arise in these estimations of the daily surface fluxes. Rutan et al. [2015] evaluated them using 8 years of in-situ observations and concluded that downward fluxes have a bias of 3.0W.m<sup>-2</sup> in the shortwave and -4.0W.m<sup>-2</sup> in the longwave. Results of the present study are given within these uncertainties.

We compute local daily climatological values for all these fields over 2000-2013 in the same way as done for BEST temperatures.

## 2.3 Automatic weather stations observations in the Sahelian Gourma (AMMA-CATCH)

The present study also uses ground-station measurements made in the Sahelian Gourma (Mali), deployed at a site which belongs to the African Monsoon Multi-disciplinary Analysis (AMMA)-CATCH network [Mougin et al., 2009].

In the following, we mostly focus on the measurement site of Agoufou, located in central Sahel, at 15°20′40″N and 1°28′45″W. Instruments are deployed in grassland, over sandy soil, which is the dominant surface type in the Malian Gourma. An automatic weather station (AWS) acquires data at a 15-min time step since April 2002, and provides air temperature, relative humidity, rainfall, wind speed and direction as well as surface radiative and turbulent fluxes.

The site is homogeneous over several kilometers, which allows a good estimate of the radiative fluxes. These data have already been used for thermodynamic and climate analyses
by Guichard et al. [2009], Timouk et al. [2009], Roehrig et al. [2013] and Lohou et al. [2014] among others.

## 2.4 CNRM-AM nudged simulation

In the present study, we use a simulation based on the atmospheric component of a prototype of the new CNRM climate model, hereafter referred to as CNRM-AM. This model is based on the version 6.2.1 of the ARPEGE-Climat atmospheric model [Déqué et al., 1994; Voldoire et al., 2013] and benefits from several significant and recently-implemented developments of the model physics parameterizations. This prototype version is similar to that used in the recent studies of Michou et al. [2015]; Leroux et al. [2016]; Martin et al. [2017].

CNRM-AM is a major update of the CNRM-CM5 atmospheric component [Voldoire et al., 2013]. It contains a prognostic turbulent kinetic energy (TKE) scheme [Cuxart et al., 2000] that improves the representation of the dry boundary layer. The new convection scheme represents in a unified way the dry, shallow and deep convective regimes, following Guérémy [2011] and Piriou et al. [2007]. The convection scheme microphysics prognostically describes cloud liquid and ice water, as well as rain and snow specific masses following the work of Lopez [2002]. It is also fully consistent with the microphysics scheme used for the large-scale condensation and precipitation. Cloud macrophysics is handled by the Ri-card and Royer [1993] scheme. The radiation scheme is based on the shortwave scheme of Fouquart and Bonnel [1980] and on the longwave Rapid Radiation Transfer Model (RRTM, [Mlawer et al., 1997]). An overview of the land surface model SURFEX can be found in Masson et al. [2013] and more details on the physical content used in the present study is described in Decharme et al. [2013, 2016]. SURFEX makes use of the ECOCLIMAP database for surface parameters [Masson et al., 2003].

CNRM-AM is a spectral model that has been used here with a T127 truncation (about 1.4° resolution at the Equator). It has 91 vertical hybrid levels up to 80 km. The first model level is near 12 m and the model has about 10 levels in the first atmospheric kilometer. It is run in an Atmospheric Model Intercomparison Project (AMIP) configuration, in which monthly-mean sea surface temperatures are prescribed and interpolated at each time step of the model. The time step is 15 min. Monthly aerosol loadings are also prescribed and constant accross each month. A climatological annual cycle is used, which is computed from the 1990-1999 period of a nudged AMIP simulation of CNRM-AM with the prognostic aerosol scheme described in Michou et al. [2015]. Note that aerosol optical properties were updated according to Nabat et al. [2013], compared to those used in CNRM-CM5.

Here, the main objective is to analyze the effects of the physical processes during the April 2010 Sahelian heatwave, without the additional complexity induced by their interactions with the large-scale dynamics. Therefore, a dynamical spectral nudging towards the 6-hourly ERA-interim reanalyzed fields [Dee et al., 2011] is applied to the wind vorticity and divergence as well as to the surface pressure, which constrains the model to follow the observed large-scale dynamical sequence [Coindreau et al., 2007]. The relaxation timescale is 12h for the vorticity and 24h for the divergence and surface pressure. To let the model physics adjusts in the surface layer, the nudging is weakened at the first four model levels (approximately up to 400 m above the ground), with no nudging at all at the first model level. Note also that the simulation started on 1 January 1979 and ended on 31 December 2012, so that the atmospheric and land-surface model spin-up can be neglected when focusing on April 2010.
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## 2.5 A conceptual prognostic model: The Surface-Atmosphere RAdiative Water vapor Impact (SARAWI) model

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A conceptual prognostic model has been specifically designed: The Surface-Atmosphere RAdiative Water vapor Impact model (SARAWI). It is used in this study to investigate the processes involved in the temperature fluctuations.

This conceptual model appears to be a useful tool to:

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- Highlight the influence of physical processes. Hereafter, the impact of the water vapor greenhouse effect is investigated, and the model allows to infer a Humidity Radiative Effect (cf sections 6.3 to 6.5);

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- Provide a simple-way to test the ability of new formulations of the physical processes to correctly reproduce observations. For instance, hereafter, a linear regression of the air emissivity is proposed in equation (9) and evaluated in section 6.1.

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- Point out the biases and sources of uncertainty in state-of-the-art models and parameterizations (hereafter, when compared to the CNRM-AM model and observations, cf sections 6.1, 6.2)

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- Perform and interpret sensitivity tests in simple and unambiguous ways for a low computational cost, contrary to complex GCM simulations (hereafter by modifying only the longwave radiative effect of low-level humidity, cf sections 6.3, 6.4)).

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### 2.5.1 Basic concepts and hypotheses

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SARAWI consists of a simple model of the soil and lower atmosphere. It aims at investigating the interactions at play between physical processes and the impact of their parameterizations on the evolution of the soil surface temperature $T_s$ and of the surface-layer air temperature $T_a$.

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SARAWI assumes that turbulence and radiative transfer are the dominant terms explaining the evolution of $T_s$ and $T_a$. The model solves local physical processes acting in the boundary-layer (turbulence and radiation transfer) by decoupling them from the regional and synoptic atmospheric processes that are either prescribed analytically or solved by an external GCM-type model and prescribed into the SARAWI model. As shown in sections 5 and 6, these hypotheses are supported by the results given by the CNRM-AM simulation, and our results suggest that this approach is sufficient to reproduce the spatial structure and temporal evolution of the 2m-air temperature $T_{2M}$, at least over North Africa during springtime 2010. The model can therefore be used to analyze the relative contributions of regional-scale circulations versus local-scale processes.

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In the SARAWI model, the soil and lower atmosphere are represented with two soil layers and one atmospheric layer, with the mass point of the atmospheric layer located at $\delta z/2$ above the ground, $\delta z$ being the atmospheric layer depth. It can be used in a one dimensional (1D) mode at a selected location, or over a given domain (hereafter all North Africa), as a light 3D model, with vertical transfers only, explicitly represented across its three layers.

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SARAWI solves three prognostic equations (one for the temperatures of each of the three layers), together with a diagnostic equation for $T_{2M}$ (details are given below). It makes use of four additional equations for the physical parameterization of fluxes and tendencies, combined with ten tuned or statistically-fitted parameterizations that account for physical properties. Finally, simulations are performed with four external input fields.
## 2.5.2 SARAWI system of equations and parameterizations

**Inputs:** SARAWI makes use of four input fields, that can be prescribed analytically or from an atmospheric model. They are indicated in the “Inputs” field in Table 1.

**Prognostic equations:** SARAWI solves three prognostic equations for $T_a$, $T_s$ and $T_{2s}$ respectively the temperatures of the atmospheric layer, the soil surface layer and the deep soil layer. They are detailed in the “Pronostic equations” field of Table 1. The different terms on the right hand sides are detailed in the “Physical parameterizations” field.

Equation (1) is the classical thermodynamic equation in which we make the assumption that the effects of shortwave radiation, parameterized convection, large-scale condensation and precipitation, and advection are negligible in the atmospheric surface layer, so that the evolution of air surface temperature is mainly driven by longwave radiation and turbulence. We will show in section 5 that this hypothesis is supported by climate-model simulations.

Equations (2) and (3) follows a simple parameterization for a two-layers soil model, using the classical force-restore method of Noilhan and Planton [1989].

The last term on the right-hand side of equation (2) is proportional to a diffusive heat flux into the deep soil layer and tends to restore $T_s$ to the mean soil temperature $T_{2s}$. $C_s$ is the inverse of the soil heat capacity. In equation (2), the latent heat flux is assumed to be negligible, which is a realistic assumption over the Sahel and Sahara at the end of the dry season (cf section 5). Equations (2) and (3) introduce a relaxation time constant ($\tau$) fixed at $\tau = 24$h, as in Noilhan and Planton [1989].

**Physical parameterizations:** Four physical parameterizations are used (cf equations (4) to (7) in Table 1). All parameters and variables present in equations (4) to (7) are detailed in Table 2.

Equations (4) and (5) correspond to classical formulations of the sensible heat flux and the net longwave flux at the surface (e.g. [Noilhan and Planton, 1989]).

The longwave radiation warming of the atmospheric layer is given by equation (6), which is a simplification of the longwave model of Mlawer et al. [1997] corresponding to a radiative balance within the atmospheric layer. Its first term corresponds to the infrared absorption by the atmospheric layer of the emitted infrared flux from the surface, and its second corresponds to the emitted infrared flux toward the surface combined with the absorbed part of that same flux reflected over the soil surface. The coefficient $h_{rad}$ is a radiative scale height (see Table 2 and section 2.5.3), which represents the height of the layer radiatively affected by the surface, in the sense that the upwelling longwave at the surface $LW_{up}$ is absorbed within the layer of height $h_{rad}$, and respectively that no longwave radiation emitted from above that layer reaches the soil surface without being absorbed. The introduction of $h_{rad}$ in equation (6) makes explicit that the transmitted incoming longwave radiation at the surface issued from above the altitude $h_{rad}$ can be neglected.

The turbulent processes are parameterized with equation (7), which is a simplification of the Mellor and Yamada [1982] turbulence scheme for a one-layer atmospheric model. The first term corresponds to a turbulent exchange with the soil surface layer and the second to a turbulent exchange with the air above the atmospheric layer.

**Diagnostic equation for $T_{2m}$:** The 2m-air temperature $T_{2m}$ is diagnosed with a linear interpolation between the soil surface temperature $T_s$ and the air layer temperature $T_a$, given by equation (8), as usual in atmospheric model. The coefficient $c_{t2m}$ typically depends on
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the static stability of the atmosphere. Here, we parameterize this coefficient according to Mahfouf et al. [1995].

<table><caption>**Table 1** The system of equations and parameterizations of the SARAWI pronostic model.</caption><thead><tr><th colspan="3">INPUTS</th></tr></thead><tbody><tr><td>(a)</td><td>SW<sub>net</sub></td><td>Net shortwave flux at the surface</td></tr><tr><td>(b)</td><td>hus</td><td>Specific humidity at the atmospheric level</td></tr><tr><td>(c)</td><td>V<sub>a</sub></td><td>Wind speed at the atmospheric level</td></tr><tr><td>(d)</td><td>T<sub>2a</sub></td><td>Temperature of the air above the SARAWI atmospheric layer (used in the parameterization of turbulence only)</td></tr><tr><th colspan="3">PRONOSTIC EQUATIONS</th></tr><tr><td>(1)</td><td>∂T<sub>a</sub> / ∂t = ∂T<sub>a</sub> / ∂t<sub>rlw</sub> + ∂T<sub>a</sub> / ∂t<sub>pbl</sub></td><td>Atmospheric layer temperature (T<sub>a</sub>) equation</td></tr><tr><td>(2)</td><td>∂T<sub>s</sub> / ∂t = C<sub>s</sub>(SW<sub>net</sub> + LW<sub>net</sub> - H) - (2π / τ)(T<sub>s</sub> - T<sub>2s</sub>)</td><td>Soil surface layer temperature (T<sub>s</sub>) equation</td></tr><tr><td>(3)</td><td>∂T<sub>2s</sub> / ∂t = (1 / τ)(T<sub>s</sub> - T<sub>2s</sub>)</td><td>Deep soil layer temperature (T<sub>2s</sub>) equation</td></tr><tr><th colspan="3">PHYSICAL PARAMETERIZATIONS</th></tr><tr><td>(4)</td><td>H = ρ<sub>p</sub>C<sub>p</sub>C<sub>h</sub>V<sub>a</sub>(T<sub>s</sub> - T<sub>a</sub>)</td><td>Surface sensible heat flux parameterization</td></tr><tr><td>(5)</td><td>LW<sub>net</sub> = σ<sub>p</sub>(ε<sub>a</sub>T<sub>a</sub><sup>4</sup> - ε<sub>s</sub>T<sub>s</sub><sup>4</sup>)</td><td>Surface net longwave flux parameterization</td></tr><tr><td>(6)</td><td>∂T<sub>a</sub> / ∂t<sub>rlw</sub> = (σ / ρ<sub>p</sub>C<sub>p</sub>h<sub>rad</sub>) {ε<sub>a</sub>ε<sub>s</sub>T<sub>s</sub><sup>4</sup> - [1 - ε<sub>a</sub>(1 - ε<sub>s</sub>)]ε<sub>a</sub>T<sub>a</sub><sup>4</sup>}</td><td>Longwave tendency parameterization</td></tr><tr><td>(7)</td><td>∂T<sub>a</sub> / ∂t<sub>pbl</sub> = K<sub>s</sub>(V<sub>a</sub>(T<sub>s</sub> - T<sub>a</sub>) / δz + K<sub>h</sub>(T<sub>2a</sub> - T<sub>a</sub>) / δz, h<sub>turb</sub>)</td><td>Turbulent tendency parameterization</td></tr><tr><th colspan="3">DIAGNOSTIC EQUATIONS</th></tr><tr><td>(8)</td><td>T<sub>2m</sub> = T<sub>s</sub> + c<sub>r2m</sub>T<sub>a</sub></td><td>2m-air temperature diagnostic</td></tr></tbody></table>

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### 2.5.3 Physiographic and physical parameters

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In equations (3) to (8), ten parameters have to be tuned, prescribed or parameterized: τ, ε<sub>s</sub>, ε<sub>a</sub>, C<sub>s</sub>, h<sub>rad</sub>, h<sub>turb</sub>, C<sub>h</sub>, K<sub>s</sub>, K<sub>h</sub> and c<sub>r2m</sub>.

Among those parameters, ε<sub>s</sub> and C<sub>s</sub> are local physiographic properties dependent on ground cover and soil texture. They have to be prescribed using soil surface characteristics
databases. C_s has a major importance since it strongly modulates the diurnal soil and air temperature ranges. ε_s is typically very close to 1.

$h_{rad}$, $h_{turb}$, $C_h$, $K_s$ and $K_h$ have to be tuned or statistically fitted, and $c_{t2m}$ requires a parameterization.

For ε_a, we propose an original and simple approach. While longwave radiative fluxes directly depends on temperature through the Stefan-Boltzman's law, longwave emissivity ε_a (and fluxes) also varies with atmospheric water vapor (e.g. [Prata, 1996]). Since the SARAWI model has been mainly designed (and will be used hereafter) to evaluate the radiative impacts of water vapor, it appears crucial that the parameterized infrared emissivity be sensitive to its variations. Similarly to Herrero and Polo [2012], we propose a simple parameterization based on a multiple linear regression:

$$ε_a = a_1 + a_2.hus + a_3.T_a \quad (9)$$

Table 2 synthesized the fixed values or parameterizations used in the SARAWI model. Note that this could be easily modified in other versions of the model in order to improve some representations of these parameters or to adjust them to other areas of the globe.

Appendix A gives details on the reasons for using values and parameterizations given in Table 2, the methodology used to infer those values and some uncertainties as compared to other parameterizations.

### 2.5.4 Configuration of the SARAWI simulations

In the present study, SARAWI simulations are made for April 2010 over North Africa, between 0° and 30°N in latitude and between 20°W and 20°E in longitude. The depth of the atmospheric layer is $δz = 25m$, the horizontal resolution is fixed to $1.4^o \times 1.4^o$ and the time step is 15-min, in order to compare results to CNRM-AM simulations.

The simulations are initialized using $T_a$ and $T_s$ from the CNRM-AM simulation on 1st April; and $T_{2s}$ is assumed to be equal to $T_s$ at the first time step (in practice, after the spin-up period, which lasts less than 24h, the precise choice of the initial field of $T_{2s}$ has no influence on our results).
PHYSIOGRAPHIC AND PHYSICAL PARAMETERS

<table><caption>**Table 2** The physiographic and physical parameters used by the SARAWI pronostic. More details are given in appendix A.</caption><thead><tr><th>Variable</th><th>Description</th><th>Fixed value or parameterization used</th></tr></thead><tbody><tr><td>ρ</td><td>Air density</td><td>ρ = 1.2 kg.m<sup>-3</sup></td></tr><tr><td>C<sub>p</sub></td><td>Air specific heat capacity</td><td>C<sub>p</sub> = 1004 J.kg<sup>-1</sup>.K<sup>-1</sup></td></tr><tr><td>σ</td><td>Stefan-Boltzman constant</td><td>σ = 5.67*10<sup>-8</sup> W.m<sup>-2</sup>.K<sup>-4</sup></td></tr><tr><td>τ</td><td>Relaxation time constant</td><td>τ = 24 h<br>(Force-restore approach of Noilhan and Planton [1989])</td></tr><tr><td>ε<sub>s</sub></td><td>Soil surface total infrared emissivity</td><td>ε<sub>s</sub> = 0.9946<br>North African average, extracted from the ECOCLIMAP database<br>([Champeaux et al., 2005; Faroux et al., 2013])</td></tr><tr><td>ε<sub>a</sub></td><td>Air total infrared emissivity</td><td>ε<sub>a</sub> = a<sub>1</sub> + a<sub>2</sub>.hus + a<sub>3</sub>.T<sub>a</sub><br>a<sub>1</sub> = 0.667, a<sub>2</sub> = 1.17.10<sup>-2</sup> with hus in g/kg and a<sub>3</sub> = 4.55.10<sup>-4</sup> with T<sub>a</sub> in °C.</td></tr><tr><td>C<sub>s</sub></td><td>Inverse of the soil heat capacity</td><td>Extracted from the ECOCLIMAP database<br>([Champeaux et al., 2005; Faroux et al., 2013]).<br>Averaged over daytime and nighttime : C<sub>s</sub><sup>night</sup> (lon, lat) and C<sub>s</sub><sup>day</sup> (lon, lat).</td></tr><tr><td>h<sub>rad</sub></td><td>Radiative scale height</td><td>h<sub>rad</sub> = c<sub>rad</sub>.δz, with c<sub>rad</sub> = 4.74</td></tr><tr><td>h<sub>turb</sub></td><td>Turbulent scale height</td><td>h<sub>turb</sub> = δz<sub>2</sub> = 35m</td></tr><tr><td>C<sub>h</sub></td><td>Drag coefficient</td><td>Daytime C<sub>h</sub> = 4.10<sup>-3</sup>. Nighttime : C<sub>h</sub> = 5.10<sup>-4</sup>.</td></tr><tr><td>K<sub>s</sub></td><td>Turbulent drag coefficient</td><td>Daytime : K<sub>s</sub> = 1.6.10<sup>-4</sup>. Nighttime : K<sub>s</sub> = 2.10<sup>-5</sup>.</td></tr><tr><td>K<sub>h</sub></td><td>Turbulent diffusivity</td><td>Daytime : K<sub>h</sub> = 0.94 m<sup>2</sup>.s<sup>-1</sup>. Nighttime : K<sub>h</sub> = 0.08 m<sup>2</sup>.s<sup>-1</sup>.</td></tr><tr><td>c<sub>r2m</sub></td><td>Static stability dependent coefficient</td><td>Based on Mahfouf et al. [1995].</td></tr></tbody></table>

3 Observed large-scale features on spring 2010

In this section, we make use of the previously described long-term observational datasets to show that the 2010 heatwave is characterized by strong positive anomalies of the daily-minimum temperatures and the incoming longwave fluxes over North Africa, correlated with positive anomalies of precipitable water.

3.1 Maps of April 2010 anomalies

In the present study, we refer to “North Africa” to describe the geographic region of Africa located between 0°N and 30°N; 20°W and 20°E. Hereafter, two subregions of interest are defined : The Sahel, as the area between 14°N and 18°N; and the Sahara, between 18° and 30°N. Both of these subregions extend from 20°W to 20°E.
Figure 1 shows April 2010 monthly means and monthly anomalies of BEST $T_{min}$ and $T_{max}$, CERES $LW_{in}$, $SW_{in}$, cloud cover fraction, AOD and PW.

In April 2010, $T_{min}$ and $T_{max}$ exhibit a springtime pattern with a maximum temperatures latitudinal band centered on the Sahel (see Figure 1a). Similarly, the maximum of $LW_{in}$ is localized over the Sahel. $SW_{in}$, cloud cover and PW exhibit distinct patterns characterized by strong meridional gradients. This highlights the contrast between the Sudano-Guinean region (south to 14°N) affected by the moist monsoon flow associated with clouds and reduced $SW_{in}$; and the Sahel and the Sahara subregions (see Figure 1a) with stronger $SW_{in}$, reduced cloud cover and enhanced dryness (low PW). The AOD pattern emphasizes a maximum over Mali, Niger and South Algeria, which are dominantly affected by dust events due to the combination of strong winds, low surface roughness, dry soils and sporadic vegetation in springtime.

Strong positive temperatures anomalies (up to 3 or 4°C) are observed in the Sahel and Sahara, particularly strong over Mauritania, Algeria and Mali. $T_{min}$ anomalies are stronger and impact a wide area, covering the western and central Sahel and Sahara (Figure 1b,d). These regions corresponds to enhanced $LW_{in}$ in April 2010, strong compared to the climatology, reaching anomalies of about 30 to 40 W/m² (Figure 1h). A strong negative $SW_{in}$ anomaly is also observed in the Sahel and Sahara, with a similar pattern to that of the $LW_{in}$ positive anomaly (Figure 1f).

Strong positive anomalies of cloud cover, AOD and PW also occur over the Sahel and Sahara in April 2010 (Figure 1j,1,n). The cloud cover increase mainly concerns the northern Sahara and is mostly related to enhanced high-level clouds (not shown). These anomalies are due to a tropical plume event, common in North Africa during spring [Knippertz and Martin, 2005; Fröhlich et al., 2013]. The tropical plume enhanced PW over Mauritania, Algeria and Libya and favored the occurrence of high clouds and low-level water vapor. PW is also increased over Mali and Burkina Faso, as the monsoon flow is anomalously north during this period. Strong AOD anomalies are located over Mali and Niger and are caused by several dust events.

## 3.2 Climatological and 2010 springtime evolution

In the following, two main climatological areas are considered: The Sahara and the Sahel, defined in the previous section. They both extend over the longitude band [20°W, 20°E] and only account for land pixels (Figure 1a).

Figure 2a,b presents the climatological and 2010 time series of $T_{min}$, $T_{avg}$ and $T_{max}$ given by BEST and averaged over each of these two areas. The 2010 springtime (March-April-May) exhibits relatively strong positive temperature anomalies, reaching 1.30°C and 1.29°C for $T_{min}$ and $T_{max}$ respectively, on average over the Sahara; and 1.26°C and 0.96°C on average over the Sahel (to be compared to a mean springtime 90% quantile value which is respectively 3.06°C, 3.59°C, 2.66°C and 2.69°C above the climatology). Over the Sahel, they occur close to their climatological annual maximum, which leads to particularly high raw temperatures.

CERES incoming radiation fluxes $SW_{in}$ and $LW_{in}$ are averaged over each domain (Figure 2c,d,e,f). Daily incoming longwave fluxes are significantly higher than shortwave fluxes (about 120W/m² on average over the period). The variability of $SW_{in}$ is driven by cloud cover and AOD fluctuations, which leads to strong synoptic and day-to-day modulations in the Sahel (Fig. 2d) whereas $LW_{in}$ corresponding variability is weaker (Fig. 2f).
<figure><img src="image_2.png" /><figcaption>**Fig. 1** Monthly-mean (left) and climatological anomalies (right) for April 2010 of $T_{max}$ (a,b), $T_{min}$ (c,d), $SW_{in}$ (e,f) and $LW_{in}$ (g,h) total cloud cover fraction (i,j), Aerosol Optical Depth (k,l) and Precipitable Water (m,n). White dotted lines in panel a) delimitates Sahel and Sahara as defined in this study. Purple cross in panel b shows the location of the Agoufou station.</figcaption></figure>
<figure><img src="image_3.png" /><figcaption>**Fig. 2** Springtime time series of (a,b) $T_{min}$ (blue), $T_{avg}$ (black) and $T_{max}$ (red); (c,d) daily-average $SW_{in}$ (black), clear-sky $SW_{in}^{clear}$ (blue), clean-sky $SW_{in}^{clean}$ (red); blue shading therefore corresponds to the Cloud Radiative Effect and orange shading to the Aerosol Radiative Effect (see section 4.1 for more details); (e,f) same as (c,d) for incoming longwave fluxes; and (g,h) Cloud fraction (in %, blue), 20*AOD+40* (red), 10*PW+60* (in cm, light blue). All values correspond to the average over the Sahara (left) or the Sahel (right). Solid lines : 2010 time series. Dashed lines : climatological time series. Grey shading : April 2010 Heatwave period.</figcaption></figure>

$SW_{in}$ anomalies, are persistently negative, near -15 W/m² on average over springtime for both domains. In contrast, $LW_{in}$ anomalies are mostly positive during the period, reaching about +18.5W/m² on average over springtime for both domains.

These anomalies are consistent with the increased cloud cover, AOD and PW observed during the period (Figure 2g,h). Variations of $SW_{in}$ are strongly coupled with the variations of cloud cover. Likewise, $SW_{in}^{clear-sky}$ is strongly related to AOD. By contrast, the fluctuations of $LW_{in}$ appear more strongly related to those of PW. These correlations are even more pronounced when restricted to the heatwave period (grey shading on Figure 2) that is further discussed in the next subsection.
3.3 Focus on the heatwave period

Recently, Barbier et al. [2018] developed a methodology to detect and track heatwaves over West Africa as intraseasonal events. They detect heatwaves when temperature intraseasonal anomalies exceed the 90% percentile of their local climatological distribution over a sufficiently extended area (greater than $6.10^5\,km^2$) for at least 3 consecutive days. For 2010, several heatwaves were identified when applying this methodology over the domain considered in the present study ($[20^\circ W, 20^\circ E]$, $[0^\circ N, 30^\circ N]$) (e.g. Day Of Year (DOY) 60-75, 100-115, 125-135, see also Figure 2 in Barbier et al. [2018]). In the following, we focus on the heatwave event which occurred between 10 and 25 April, i.e. DOY 100 and 115. A significant part of the domain (about $24.10^5\,km^2$, i.e. 20% of the domain) was affected by this long-lasting event and furthermore, it occurred when temperatures were very high over the Sahel (Fig. 2b). Hereafter, this period is referred to as the heatwave period (HW, grey shading in Figures). Note that the details of physical processes and mechanisms at play during springtime North African heatwaves are likely to vary from one event to another; in particular when considering late winter events (occurring in a very dry environment) or early monsoon events in late June (when the atmospheric water amount is on average higher). The period on which we focused here is more representative of North African heat waves occurring during the spring period when temperatures reach their annual maxima in the Sahel.

Increased $T_{min}$ and $T_{max}$ (and therefore $T_{avg}$) anomalies occur during this heatwave period, up to $4^\circ C$ over both the Sahel and Sahara. They coincide with reduced $SW_{in}$ (anomalies up to $-49\,W/m^2$) and strongly enhanced $LW_{in}$ (anomalies up to $+44\,W/m^2$). Note that the heatwave more strongly affects $T_{min}$, and is slightly stronger over the Sahara.

Temporal correlation coefficients between all the fields shown in Figure 2, both during the heatwave and pre-heatwave periods, are indicated in Table 3. Whereas all these fields display marked anomalies during the heatwave, day-to-day fluctuations are strongly positively correlated ($r > 0.8$ on both the Sahel and Sahara) only between $T_{min}$ and $LW_{in}$, $T_{min}$ and PW, $LW_{in}$ and PW; (see bold values in Table 3). This suggests a tight link between nighttime temperatures, incoming longwave fluxes and precipitable water, both over the Sahel and Sahara, while every other covariations are less relevant. Note that during the pre-heatwave 40 days spingtime period, these three correlations are significantly lower than during the heatwave period. This is particularly true over the Sahara where the strong link between PW and $LW_{in}$ or $T_{min}$ appears to be limited to the heatwave period. This highlights the impact of humidity during the heatwave, that will be further explored with the CNRM-AM and SARAWI models in section 5 and 6. Table 3 also highlights that cloud cover has a direct influence on the reduction of $SW_{in}$, which is expected.

Positive correlations are also found between cloud cover and $LW_{in}$ (or $T_{min}$), on average over both the Sahel and Sahara. Similarly, a significant positive correlation is found between AOD and $LW_{in}$ (or $T_{min}$), but only over the Sahel (the correlation being negative over Sahara). However, these correlations should be interpreted with care. Indeed, cloud and aerosol longwave effects, that will be further explored in section 4, will be shown to be unable to explain $LW_{in}$ anomalies. Rather, these correlations are explained by covariations between PW and cloud cover (correlation of about 0.65), and between AOD and cloud cover over the Sahel (correlation of 0.74, due to the occurrence of dust events in Eastern Sahel and cloud intrusions in Western Sahel at the same time, not shown).

$T_{max}$ fluctuations are not easily related to either incoming radiation fluxes, clouds, PW or aerosols. They are positively correlated with $SW_{in}$ over the Sahara, while - surprisingly - negatively correlated over the Sahel during the heatwave. $T_{max}$ fluctuations are also negatively correlated with cloud cover and AOD over Sahara, but positively over the Sahel. This
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suggests that $T_{max}$ variations are probably explained by a complex interplay between various processes operating at different scales.

In summary, the April 2010 heatwave emerges from the climatology mainly because of the very high $T_{min}$ prevailing during this 15-day period, while high $T_{max}$ are restricted to a shorter duration (10 days) with weaker departure from the 90% percentile threshold. In the following, we focus mainly on the understanding of $T_{min}$ anomalies.

<table><caption>**Table 3** Correlation coefficient *r* between two fields given in the left column over the Sahel (columns 2 and 4) and the Sahara (columns 3 and 5) during the heatwave period (10 to 25 April, column 2 and 3) and during the pre-heatwave springtime period (1 March to 10 April, columns 4 and 5). Values in parentheses are the correlation coefficient in terms of anomalies instead of raw values. Strongest correlations ($|r| > 0.8$ on both domains) are underlined with bold characters.</caption><thead><tr><th rowspan="2">Couples of variables</th><th colspan="2">HEATWAVE</th><th colspan="2">PRE-HEATWAVE</th></tr><tr><th>SAHEL</th><th>SAHARA</th><th>SAHEL</th><th>SAHARA</th></tr></thead><tbody><tr><td>$T_{min}$ and $LW_{in}$</td><td><strong>0.97 (0.94)</strong></td><td><strong>0.85 (0.74)</strong></td><td>0.74</td><td>0.87</td></tr><tr><td>$T_{min}$ and $SW_{in}$</td><td>-0.84 (-0.86)</td><td>0.01 (-0.46)</td><td>-0.20</td><td>0.55</td></tr><tr><td>$T_{min}$ and AOD</td><td>0.82 (0.87)</td><td>-0.73 (-0.57)</td><td>0.22</td><td>-0.09</td></tr><tr><td>$T_{min}$ and Cloud cover</td><td>0.77 (0.64)</td><td>0.37 (0.62)</td><td>0.16</td><td>0.59</td></tr><tr><td>$T_{min}$ and PW</td><td><strong>0.84 (0.74)</strong></td><td><strong>0.85 (0.76)</strong></td><td>0.60</td><td>0.11</td></tr><tr><td>$T_{max}$ and $LW_{in}$</td><td>0.62 (0.47)</td><td>0.22 (-0.09)</td><td>0.24</td><td>0.73</td></tr><tr><td>$T_{max}$ and $SW_{in}$</td><td>-0.43 (-0.23)</td><td>0.53 (0.30)</td><td>0.43</td><td>0.76</td></tr><tr><td>$T_{max}$ and AOD</td><td>0.59 (-0.39)</td><td>-0.69 (-0.45)</td><td>-0.40</td><td>-0.24</td></tr><tr><td>$T_{max}$ and Cloud cover</td><td>0.25 (-0.03)</td><td>-0.30 (-0.24)</td><td>0.01</td><td>0.43</td></tr><tr><td>$T_{max}$ and PW</td><td>0.36 (0.15)</td><td>0.25 (-0.04)</td><td>0.29</td><td>-0.09</td></tr><tr><td>$LW_{in}$ and AOD</td><td>0.82 (0.85)</td><td>-0.62 (-0.31)</td><td>0.69</td><td>0.28</td></tr><tr><td>$LW_{in}$ and Cloud cover</td><td>0.75 (0.49)</td><td>0.70 (0.93)</td><td>0.55</td><td>0.67</td></tr><tr><td>$LW_{in}$ and PW</td><td><strong>0.87 (0.82)</strong></td><td><strong>0.95 (0.86)</strong></td><td>0.72</td><td>0.11</td></tr><tr><td>$SW_{in}$ and AOD</td><td>-0.91 (-0.92)</td><td>-0.31 (-0.24)</td><td>-0.80</td><td>-0.33</td></tr><tr><td>$SW_{in}$ and Cloud cover</td><td><strong>-0.82 (-0.72)</strong></td><td><strong>-0.82 (-0.87)</strong></td><td>-0.57</td><td>0.07</td></tr><tr><td>$SW_{in}$ and PW</td><td>-0.66 (-0.61)</td><td>-0.16 (-0.44)</td><td>-0.49</td><td>-0.37</td></tr></tbody></table>

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## 3.4 Significant $LW_{in}$ positive anomalies in $T_{min}$ heatwave areas

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The previously described strong positive correlation between daily-mean values of $LW_{in}$ and $T_{min}$ (or their anomalies, cf Table 3) remains true at different time scales: spatially-averaged over the Sahel and Sahara, the correlation coefficient reaches $r = 0.99$ over the annual cycle, 0.96 over springtime and 0.90 over April 2010. This correlation can be further analyzed in space with Figure 3, which shows $LW_{in}$ anomalies for each day of the heatwave, overlaid by areas affected by the $T_{min}$-heatwave (in black contours). Strong $T_{min}$ positive anomalies tend to overlay strong $LW_{in}$ positive anomalies (up to $44W/m^2$), both over the Sahel and Sahara.

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This relationship is however weaker over the Sudano-Guinean area, south to $12^\circ$N, which is the approximate location of the InterTropical Discontinuity (ITD) during springtime. There, $T_{min}$ can reach anomalously-high values, with moderate $LW_{in}$ anomalies (despite high $LW_{in}$ raw values). This suggests that surface incoming longwave fluxes in the moister and wetter April Sudano-Guinean climate are less sensitive to fluctuations of water vapor and cloud cover than the driest April climate of Sahel and Sahara, in agreement with e.g. Stephens et al. [2012].

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This also points out to distinct processes and mechanisms leading to heatwaves in the Sudano-Guinea region, while the link with $LW_{in}$ clearly dominates in the Sahel and Sahara. Hereafter, we focus on the Sahel and Sahara.
<figure><img src="image_4.png" /><figcaption>**Fig. 3** Maps of the anomalies of the CERES daily incoming longwave flux, $LW_{in}$ (color shading) superimposed with the areas affected by the heatwave, i.e. where $T_{min}$ exceeds its local daily 90% percentile threshold (black dots), from 10 to 24 April 2010.</figcaption></figure>

## 4 Cloud and aerosol radiative effects

Here, we explore the radiative impacts of clouds and aerosols and show that, although strong positive anomalies of AOD and cloud cover are found respectively over the Sahel and Sahara, their radiative impacts are too weak to explain the anomalies of longwave fluxes.

### 4.1 Quantification of the Cloud Radiative Effect (CRE) and Aerosol Radiative Effect (ARE)

For any radiative flux $F$, the CERES database provides an estimate of the corresponding clear-sky (ie cloud free) $F_{clear-sky}$ and clean-sky (ie cloud and aerosol free) $F_{clean-sky}$ computed fluxes.
Following the definition of Ramanathan et al. [1989], the Cloud Radiative Effect (CRE) can be expressed as:

$$ CRE = F - F_{\text{clear-sky}} \qquad (10) $$

and similarly for the Aerosol Radiative Effect (ARE):

$$ ARE = F_{\text{clear-sky}} - F_{\text{clean-sky}} \qquad (11) $$

The Total Radiative Effect (TRE) is then:

$$ TRE = CRE + ARE \qquad (12) $$

## 4.2 Daily Radiative Effects during the heatwave

Figure 4 illustrates the daily-mean CRE and ARE in both the shortwave and longwave bands for 15 April 2010, i.e. doy 105.

That day, the total cloud fraction is high over the northern Sahara, and the AOD is particularly strong over Niger, Eastern Mali and Southern Algeria (Figure 4a,b).

Cloud cover and dust loadings both reduce incoming shortwave radiative fluxes at the surface, leading to negative shortwave CRE and ARE (Figure 4c,d). In contrast, the incoming longwave radiative flux at the surface is increase below clouds and high dust loadings, leading to positive CRE and ARE, up to several tens of $W/m^2$ in these areas (Figure 4e,f). This emphasizes how both aerosols and clouds can have a strong radiative impact over West Africa in spring.

## 4.3 Day-to-day evolution of ARE and CRE during the heatwave

On average over both the Sahel and the Sahara, raw values of ARE are stronger than CRE both in the shortwave and longwave bands (Figure 5). $SW_{in}$ is reduced by about $20W/m^2$ with clouds and by another $50W/m^2$ with dust loadings. Conversely, $LW_{in}$ is increased by about $10W/m^2$ with clouds and by another $25W/m^2$ with dust loadings.

During the whole spring 2010, large negative anomalies of shortwave ARE and positive anomalies of longwave ARE are observed, both over the Sahel and Sahara (Figure 5). This is consistent with the positive anomaly of AOD (red curves in Figure 2g,h) that increases both shortwave cooling and longwave warming. A few strong dust events occur during this period, for instance between DOY 75 and 80, when ARE reduces $SW_{in}$ by $-90W/m^2$ and increases $LW_{in}$ by $+55W/m^2$ over the Sahel. The heatwave period (grey shading in Figure 5) is however less affected by the ARE over the Sahara (with anomalously low values in the longwave) and only slightly affected by a positive ARE anomaly over the Sahel, at the end of the period, between DOY 110 and 115.

Clouds have a lower radiative impact, both on longwave and shortwave fluxes, and the only significant CRE negative anomaly is observed in the shortwave over Sahara during the heatwave (where it is driven by the tropical plume event) and over the Sahel at the end of the heatwave period. The longwave CRE remains close to its climatological values, without any notable anomaly during the heatwave.
<figure><img src="image_5.png" /><figcaption>**Fig. 4** Cloud cover area (%) (a) and AOD (b), CRE (c) and ARE (d) for SWin (in W/m²), CRE (e) and ARE (f) for LWin (in W/m²), over North Africa given by CERES on 15 April 2010, i.e. doy 105.</figcaption></figure>

## 4.4 Cloud and Aerosol contributions to radiative anomalies

The ARE and CRE anomalies, together with the resulting TRE anomalies are compared to the incoming radiative flux anomalies in Figure 6. For each region, the fraction of the incoming flux anomalies explained by either clouds or aerosols or the combination of the two is analyzed. Note that, since clouds reduce SWin (cf Figure 5), a negative (respectively positive) anomaly of shortwave CRE does not correspond to a lower *radiative impact*, but means that clouds produce a *stronger reduction* (respectively a lower reduction) of the incoming fluxes in 2010 than usual at the same day. Similarly, since clouds increase LWin, a positive (resp. negative) anomaly of longwave CRE means that clouds produce a stronger increase
<figure><img src="image_6.png" /><figcaption>**Fig. 5** springtime time series of incoming shortwave (a,b) and longwave (c,d) ARE (red) and CRE (blue), spatially averaged over the Sahara (left) and the Sahel (right). Solid lines: 2010. Dashed lines: climatology. The vertical dashed green line indicates 15 April 2010, shown in Figure 4.</figcaption></figure>

(resp. a lower increase) of the incoming fluxes in 2010 than usual at the same day. Same conclusions can be dressed for ARE.

During the heatwave, a strong negative anomaly of *SW*<sub>in</sub> is observed (Figure 6a,b). It is almost entirely explained by clouds over the Sahara, and by a combined effect of clouds and aerosols in the Sahel (with a larger contribution from aerosols though). Note that the 15-day period following the heatwave is also marked by a strong negative anomaly of *SW*<sub>in</sub>, which, in contrast, is almost entirely explained by aerosols in the Sahara.

The heatwave is characterized by a wide and strong positive anomaly of $LW_{in}$ (about 25W/m$^2$ in the Sahara and 30W/m$^2$ in the Sahel, cf Figure 6c,d). CERES surface radiative fluxes estimates do not support that clouds and aerosols might drive this positive anomaly, as they even contribute to a negative anomaly over the Sahara and to a very weak ARE positive anomaly of 1.5W/m$^2$ over the Sahel, which roughly corresponds to only 5% of the total $LW_{in}$ anomaly. Conversely, this anomaly of $LW_{in}$ is strongly correlated to that of PW (Table 3 and Figure 6e,f), which suggests that the radiative effect of water vapor contributes to the emergence of this $LW_{in}$ anomaly. This water vapor radiative effect will be further investigated in details with the SARAWI model in section 6.
<figure><img src="image_7.png" /><figcaption>**Fig. 6** springtime time series of anomalies of: shortwave fluxes and shortwave ARE, CRE, TRE (a,b), long-wave fluxes and longwave ARE, CRE, TRE (c,d), cloud fraction, AOD and PW (e,f), averaged over the Sahara (left) and the Sahel (right).</figcaption></figure>

## 5 Nudged climate model simulation results

In this section, boundary-layer physics is explored using climate simulations performed with CNRM-AM. We show that the 2m-temperature is driven by turbulence and longwave radiation, and that the latter drives its nighttime evolution. Atmospheric longwave emissivity is found to be closely related to 2m-specific humidity.

### 5.1 Maps of fluxes and temperature during the heatwave

The dynamical nudging towards ERA-interim fields prevents strong departures of the CNRM-AM simulation from observations and allows to follow the realistic chronology of the heat-waves events. Indeed, the annual cycles of $T_{min}$ and $T_{max}$ and their spatial variability over North Africa are well correlated to observed values (the mean correlation coefficient over the 222 SYNOP ground-stations included in the considered domain is around 0.75 for $T_{min}$ and $T_{max}$). The annual averaged bias over these stations remains also small, -0.06°C for $T_{min}$ and -0.4°C for $T_{max}$. Note that, at smaller-scale, biases nevertheless become larger. For instance, in the Sahelian belt during the heatwave, $T_{min}$ is underestimated (up to 2.5°C) at some ground-stations.
<figure><img src="image_8.png" /><figcaption>**Fig. 7** Incoming shortwave flux *SW*<sub>in</sub> (a,b) and longwave flux *LW*<sub>in</sub> (c,d) at the surface in W/m<sup>2</sup>; *T*<sub>max</sub> (e,f) and *T*<sub>min</sub> (g,h) in °C over North Africa given by CERES or BEST observations (left) and CNRM-AM simulation (right) on 15 April 2010, ie doy 105. Note that there is no data in ocean on panels e and g.</figcaption></figure>

In line with the results of Sane et al. [2012]; Hourdin et al. [2015]; Diallo et al. [2017] which also constrained the atmospheric dynamics of their GCM simulations by a high-frequency nudging of the wind towards meteorological reanalyses, our CNRM-AM nudged simulation is also able to capture the main observed spatial patterns at a daily time scale. A typical comparison between the observed and simulated daily-mean *SW*<sub>in</sub> and *LW*<sub>in</sub> fluxes, *T*<sub>max</sub> and *T*<sub>min</sub> temperatures is shown in Figure 7, for 15 April 2010 (same day as Figure 4).

The main features of the incoming fluxes and radiative effects of clouds (dominantly present in Northern Sahara, Figure 7) are well-captured by CNRM-AM (Figure 7a,b,c,d), especially in terms of spatial patterns. Similarly, *T*<sub>max</sub> patterns are well reproduced, with the hottest areas located in the Sahel and southern Sahara and the colder area near the western Saharan coast (Figure 7e,f). The strong *T*<sub>min</sub> values are also reasonably simulated, both over Mali and the northern Sahara, consistently with the realistic simulation of the strong nighttime *LW*<sub>in</sub> (partly due to the high-level clouds present that day, Figure 4a).
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However, some biases can be noticed, mainly located in Niger and Chad, where $SW_{in}$ is overestimated and $LW_{in}$ underestimated. These biases could be related to AOD differences. Indeed, CNRM-AM uses a climatological monthly-mean AOD, whereas AOD on that day (15 April 2010) exhibits a strong anomaly over these areas (Figure 4b). As a consequence, the strong observed longwave and shortwave ARE are most likely missed by the model on this day, which leads to overestimated $T_{max}$ and underestimated $T_{min}$ over Niger and Chad (Figure 7f,h).

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## 5.2 Fluctuations of temperature, humidity and fluxes in the Sahel during the heatwave: comparison with in-situ data

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A comparison between simulated and observed time series of temperature, specific humidity and radiative fluxes is presented in Figure 8, at Agoufou, Mali (see location in Figure 1b), within the Sahelian area significantly affected by the heatwave (Figure 3). Here, we used the simulated fields at the closest grid point to the observational site (15°20′40″N and 1°28′45″W).

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Before DOY 103, Agoufou is located north of the ITD, the low-atmospheric layers are dry ($q_v < 3g/kg$) and the surface air temperature is high during daytime (> 40°C) but sharply drops at night, down to 23°C. (Figure 8a). $SW_{in}$ is strong during daytime while $LW_{in}$ (and $LW_{net}$) decreases to relatively low values during nighttime (Figure 8b,d,e). The Diurnal Temperature Range (DTR) is large, around 20°C before DOY 103.

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In-situ observations at Agoufou in 2010 illustrate the impact of the arrival of the monsoon flow in the Sahelian belt (this flow migrates northward during springtime, [Couvreux et al., 2010]): its first incursion occurs on DOY 103. Once the flow has reached the site, atmospheric water vapor increases, and simultaneously, nighttime temperatures, $LW_{in}$ and $LW_{net}$ increases ($T_{min} > 30°C$). The following 12 days match the local heatwave period, during which daytime $SW_{in}$ is reduced and displays a much stronger day-to-day variability due to the cloud cover. It leads to much lower $T_{max}$ and DTR during cloudy days. During clear-sky days, DTR is significantly reduced compared to the pre-heatwave period while $T_{max}$ remains close to its pre-heatwave values (40-45°C). The daily-average temperature increase is dominantly driven by that of $T_{min}$ during this heatwave, whereas $T_{max}$ is only weakly affected by the change of environmental air masses.

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The incursions of the monsoon flow, as seen by the increase of 2-m specific humidity are correctly reproduced by CNRM-AM (dotted lines in Figure 8a). The dynamical nudging thus allows to well constrain the location of the ITD, at least around Agoufou. Consistently, the increase of $T_{min}$ concomitant with this moistening is also realistically captured, with $T_{min}$ increasing by about 10°C between the pre-heatwave and the heatwave periods. The simulated diurnal fluctuations of radiative fluxes, specific humidity and temperatures are also close to observations, despite some biases, most likely due to the representation of clouds and can be summarized as follows:

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1. Day-to-day variability of $SW_{in}$ is underestimated during the heatwave period (especially during the cloudy period from day 107 to 112, Figure 8b). Since shortwave CRE seems reasonably well reproduced with CNRM-AM (not shown), this overestimation of $SW_{in}$ points towards either an underestimation of the cloud cover at this site, or an incorrect phasing in the diurnal cycle of cloud cover.

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2. Consistently, the DTR is overestimated during the heatwaves cloudy days.
<figure><img src="image_9.png" /><figcaption>**Fig. 8** Time series of: a) 2-m air temperature (black) and specific humidity (blue); b) *SW*<sub>in</sub> (red) and *SW*<sub>up</sub> (green); c) *LW*<sub>in</sub> (red), *LW*<sub>up</sub> (green) and *LW*<sub>net</sub> (blue) at Agoufou during the heatwave. Solid lines: Local ground observations. Dotted lines: CNRM-AM simulation.</figcaption></figure>

3. Finally, *LW*<sub>in</sub> is underestimated throughout the diurnal cycle, while *LW*<sub>up</sub> is closer to observations, except for cloudy days for which the simulated *SW*<sub>in</sub> leads to an overestimation of the land surface temperature and *LW*<sub>up</sub>. Their combination induces an underestimated *LW*<sub>net</sub>, more pronounced during cloudy days.

Even though it remains difficult to draw firm conclusions regarding the role of cloud during the heatwave, especially because of the shortcomings resulting from the comparison between local measurements and a model grid pixel of 1.4°, CNRM-AM is able to capture part of the major observed characteristics of the *T*<sub>min</sub> and *LW*<sub>in</sub> evolutions, especially their synchronous increase when the monsoon flow reaches Agoufou. CNRM-AM can thus be used to further understand part of the role of water vapor in the *T*<sub>min</sub> evolution. Note however that the increase in *T*<sub>min</sub> and *LW*<sub>in</sub> are weaker in CNRM-AM, which suggests an underestimation of the impact of humidity on 2m-temperatures and longwave fluxes. The SARAWI model will be used in section 6 to further explore this humidity impact.
## 5.3 Physical processes acting at local scale : the impacts of turbulence and longwave radiation

In order to investigate the processes at play in the low atmospheric layers, we analyze the daytime and nighttime temperature budgets in the first atmospheric layer of the CNRM-AM simulation. Figure 9 shows the daytime and nighttime variations of temperatures for each day of April 2010 (purple) at gridpoint nearest to Agoufou, together with the contribution of each physical process: boundary-layer turbulence, longwave and shortwave radiation, large-scale precipitation and condensation, parameterized deep and shallow convection, and advection, that correspond to the contributions of the different processes to the thermodynamics equation (here, they are cumulated either over the daytime hours, i.e. from sunrise to sunset, or nighttime hours). The total temperature variation (purple) is the sum of each of the previously listed contributions.

The CNRM-AM nocturnal cooling is almost entirely due to longwave radiation (Figure 9b), whereas its daytime warming mainly results from the balance between the longwave radiative warming and the turbulent cooling (Figure 9a). Surprinsingly, during daytime, the longwave warming dominates the temperature variation at the first atmospheric level and overcompensates the turbulence. The net daytime effect of turbulence is to cool the first atmospheric level. This cooling mainly acts in the afternoon by vertical mixing of the first layer with the colder layers above (more details in section 6.1 and Figure 11). The temperature advection only plays a minor role in the evolution of the first air layer temperature. Therefore, the fluctuations of surface air temperature during the heatwave episode are dominantly driven by longwave radiative and turbulent processes.

Figure 10a,b illustrates the evolution of the nighttime surface energy budget. This nighttime budget is dominated by the net radiative cooling $R_{net} = LW_{net}$, and very slightly compensated with a weak warming from the surface by the sensible heat flux (Figure 10a). Note that, after DOY 103, when the ITD overpasses Agoufou, the nighttime net cooling $R_{net}$ weakens, compared to the pre-heatwave period. Both $LW_{in}$ and $LW_{up}$ increase, but $LW_{in}$ increases more than $LW_{up}$, which leads to an increase in $LW_{net}$ and enhances the radiative coupling between the surface and the lower troposphere. This further induces a weaker nighttime cooling of the lower atmospheric layer (Figure 9b).

## 5.4 Impact of water vapor on atmospheric longwave emissivity

The land surface longwave emissivities $\epsilon_s$ can be retrieved from:

$$LW_{up} = \sigma \cdot \epsilon_s \cdot T_s^4 \qquad (13)$$

We can also estimate an atmospheric “effective” longwave emissivity $\epsilon_a$ from $LW_{in}$ and the temperature of the lower layer (e.g. [Prata, 1996] among others), using:

$$LW_{in} = \sigma \cdot \epsilon_a \cdot T_a^4 \qquad (14)$$

Figure 10c illustrates the April 2010 time series of the nighttime values of $\epsilon_s$ (red) and $\epsilon_a$ (black), computed from CNRM-AM fields. The evolution of this air longwave emissivity $\epsilon_a$ at Agoufou is strongly correlated ($r = 0.94$) with the nighttime average $2m$ specific humidity (Figure 10c,d). Note that this correlation still holds at smaller time-scales (not shown). It illustrates the increase of longwave emissivity associated with an increase of the amount of water vapor. The time series of $\epsilon_a$ is well-approximated by the linear regression using $2m$
<figure><img src="image_10.png" /><figcaption>**Fig. 9** Time series of daytime (a) and nighttime (b) $\Delta T$ temperature variation at the first atmospheric level (purple) and the corresponding contribution of each physical parameterization during April 2010 at Agoufou, in CNRM-AM simulation. Black: planetary boundary layer (pbl); blue: radiative longwave (rlw); green: radiative shortwave (rsw); grey: large-scale condensation and precipitation (lscp); red: deep and shallow convection (conv); orange: advection (adv).</figcaption></figure>

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specific humidity and 2m air temperature presented in equation 9 (with values of $a_i$ fitted at Agoufou, blue curve in Figure 10c).
<figure><img src="image_11.png" /><figcaption>**Fig. 10** Time series of nighttime surface fluxes H, LE and $LW_{net}$ (a), $LW_{in}$ and $LW_{up}$ (b), $\epsilon_s$, $\epsilon_a$ and parameterized $\epsilon_d$, cf section 5.4 (c), and 2m specific humidity (d) in April 2010 at Agoufou, in the CNRM-AM simulation.</figcaption></figure>

# 6 Insights from a conceptual prognostic model : quantification of a Humidity Radiative Effect (HRE)

Here, the SARAWI model presented in section 2.5 is used to investigate further the impact of water vapor. To this end, we introduce a Humidity Radiative Effect (HRE, detailed in subsection 6.3). SARAWI explicitly parameterizes the effect of water vapor on the air longwave emissivity (equation 9).

This model assumes that synoptic and regional scale motions associated with the monsoon flow and the tropical plume can be decoupled from physical processes operating at local scale, and therefore the CNRM-AM wind and specific humidity fields are used as inputs to the SARAWI model. Then, the model directly solves the effects of turbulence and radiative transfer between the soil and the atmospheric surface layer, as these two processes have been identified as the major drivers of the temperature fluctuations (section 5).

Simulations are performed with SARAWI over April 2010, either in 1D at the site of Agoufou, and in 3D over North Africa.
In the following, we first evaluate the time evolution of the SARAWI variables given in equations (1) to (8) with the help of the CNRM-AM simulations (section 6.1) before evaluating the 3D SARAWI computation over North Africa (section 6.2). Then, another simulation is made with a constant specific humidity field to evaluate an HRE at Agoufou during the heatwave (section 6.3), and over North Africa (section 6.4). Finally, we demonstrate that the observed anomaly of $LW_{in}$ in North Africa can be explained by means of the HRE quantified with SARAWI (section 6.5).

## 6.1 Evaluation of the representation of turbulence and longwave radiation

Figure 11 presents a comparison of the time evolution of $\frac{\partial T_a}{\partial t_{rlw}}$, $\frac{\partial T_a}{\partial t_{pbl}}$, $LW_{net}$ and $H$ simulated by CNRM-AM and SARAWI at Agoufou, zoomed over a 5-day window during the heatwave period. This period is centered around DOY 103, which corresponds to the first incursion of the monsoon flow at the site. It is chosen to point out the evolution of the diurnal cycles during the transition from the pre-heatwave towards the heatwave period, but a similar good match between SARAWI and CNRM-AM outputs is found throughout April 2010 (see Figure 13 detailed in the following sections).

Indeed, SARAWI faithfully replicates the diurnal fluctuations simulated by CNRM-AM, for the four parameterized fluxes and temperature tendencies. Similarly, time series of $T_s$, $T_{2m}$ and $T_a$ given by SARAWI are very close to those computed by CNRM-AM (Figure 11e,f), with only minor deviations (the mean biases over April 2010 are 0.15°C, 0.5°C and 0.9°C respectively for $T_a$, $T_{2m}$ and $T_s$, with $r > 0.98$ for all three temperatures).

SARAWI also reproduces quite well the transition between the pre-heatwave regime (higher DTR, stronger nighttime air radiative cooling, lower daily-mean $LW_{net}$) and the heat-wave regime (lower DTR, lower nighttime air radiative cooling, higher $LW_{net}$). This ability of SARAWI to reproduce this transition points out the crucial impact of atmospheric water vapor on longwave air emissivity, and thus on the increase of temperature and fluxes. From these results, the following scenario, which implies a water vapor greenhouse effect, can be formulated:

1. The increase of specific humidity associated with the monsoon flow increases $\epsilon_a$, that in turn increases $LW_{in}$.

2. This increase of $LW_{in}$ increases the radiative warming of the soil surface layer, and thus also $T_s$ (Figure 11e)

3. Synchronously, the increase of $T_s$ leads to an increase of $LW_{up}$.

4. $LW_{in}$ however increases more than $LW_{up}$, which leads to an increase of $LW_{net}$ (Figure 11c).

5. The increase of $LW_{in}$ corresponds to a loss of energy for the air layer, but this loss is more than compensated by an increased infrared absorption of $LW_{up}$ in this layer. Indeed, the latter is enhanced by both higher $LW_{up}$ and air absorptivity (equal to $\epsilon_a$); whereas the former is solely increased by higher $\epsilon_a$.

6. This finally results in less nighttime radiative cooling of the air layer and therefore in a higher $T_a$ in the heatwave period than before.

This water vapor greenhouse effect involves a positive feedback: higher $LW_{in}$ leads to a warmer surface, which in turn leads to a warmer air layer, and therefore higher $LW_{in}$. The magnitude of this feedback is limited as higher $LW_{in}$ also means a loss of energy of the air layer, which negatively feeds back on $T_a$. The resulting heatwave equilibrium involves a
<figure><img src="image_12.png" /><figcaption>**Fig. 11** Time series of $\frac{\partial T_a}{\partial t_{rlw}}$ (a), $\frac{\partial T_a}{\partial t_{pbl}}$ (b), $LW_{net}$ (c), $H$ (d), $T_s$ (e) and $T_a$ (f, dotted lines) and $T_{2m}$ (f, solid lines) for 5 days of the heatwave at Agoufou, in SARAWI (red) and CNRM-AM simulation (black). Blue dots at the top or bottom of panels indicate the presence of clouds in CNRM-AM. Observed $LW_{net}$ and $T_{2m}$ are superimposed in green in panels c) and f) respectively.</figcaption></figure>

balance between these two feedbacks, which happens on a very short timescale, during the first heatwave night.

SARAWI exhibits few departures from CNRM-AM, mainly during the night of DOY 104, due to the presence of clouds in the CNRM-AM simulation (cf blue dots in Figure 11). Cloud longwave radiative effects are not represented in the SARAWI model, and that night, the presence of clouds is associated with enhanced $LW_{in}$ in CNRM-AM, which leads to higher $T_s$ and $T_{2m}$ than in SARAWI (the differences reaches up to $3^\circ C$). Interestingly, these SARAWI biases provide inferences on the longwave CRE both on fluxes and temperatures.

Finally, the available observations at Agoufou are superimposed in blue in Figure 11. The observed $LW_{net}$ is underestimated by both CRNM-AM and SARAWI due to an underestimation of $LW_{in}$, throughout the diurnal cycle, as discussed in section 5.2. Nevertheless, the observed $T_{2m}$ is quite well reproduced with CNRM-AM and SARAWI, except towards the end of the night. This can be explained as follows: the daytime underestimation on $LW_{net}$ has a low impact of $T_{2m}$ since shortwave fluxes are significantly stronger so that the daytime energy budget is dominated by shortwave which is correctly reproduced with these models. However, the nighttime underestimation of $LW_{net}$ leads to a stronger cooling and therefore to
<figure><img src="image_13.png" /><figcaption>**Fig. 12** *T*<sub>min</sub> (a,b) and *LW*<sub>net</sub> (c,d) fields given by SARAWI (left) and CNRM-AM (right) on 15 April 2010, ie day 105.</figcaption></figure>

a slightly underestimated end-of-night T$_{2m}$. Note that the underestimation of LW$_{in}$ is due to an underestimation of ε$_{a}$, which could be solved in SARAWI if equation (9) was regressed with observed data, rather than with CNRM-AM data as done in the current version of the model.

6.2 Maps of T_min and longwave fluxes over North Africa

SARAWI is further used in a 3D mode over North Africa. The main geographical patterns of T_min and LW_net given by CNRM-AM are well reproduced by SARAWI. An example is shown in Figure 12 for 15 April 2010. Similar results are found for every days of April.

The most notable biases are found in the northern Sahara for $T_{min}$ and $LW_{net}$, which are most likely related to the neglect of longwave CRE in SARAWI. There, the cloud cover is high in both observations and CNRM-AM, and induces significant longwave CRE and nighttime warming (Figures 4 and 7).

Apart from those cloud-related impacts, the agreement between CNRM-AM and SARAWI over the region, both in terms of patterns and orders of magnitude, validates the hypotheses at the heart of the SARAWI model, and underlines the nature of the scale interactions between large-scale circulations and local physical processes: the dynamics of the monsoon flow and that of the tropical plume event over the Sahara, drive regional and synoptic-scale advection of atmospheric water vapor. From there, radiative and turbulent processes, which act at local and subdiurnal scales, subsequently drive the evolution of the longwave fluxes, soil and low-level air temperatures.

In summary, the high nighttime temperatures observed during the heatwave do not result from some synoptic advection of warm air masses (since synoptic advection is neglected in equation (1)). Rather, the synoptic advection of water vapor is the most important component
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as it increases the low-level air opacity and emissivity (that explicitely depends upon the specific humidity, which is prescribed in SARAWI, through equation (9)). This results in an increase of $T_{min}$, which is dominantly controlled by atmospheric radiative transfer and boundary-layer turbulence, since they are the only processes parameterized in SARAWI (equation (1)).

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## 6.3 Quantification of the Humidity Radiative Effect (HRE)

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Figure 13 shows, for April 2010 at Agoufou, time series of $LW_{in}$ (a), $T_{2m}$ (b), $T_{max}$ (c, dashed lines) and $T_{min}$ (c, solid lines) computed by SARAWI (red), and CNRM-AM (black). The high correlation between the CNRM-AM and SARAWI time series echoes the results presented in the previous section. Differences between CNRM-AM and SARAWI only occur during the most heavily cloudy days (blue dots in Figure 13).

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An additional 3D simulation is performed with SARAWI where specific humidity remains constant in time; for each grid point, it equals its nighttime average value on 1 April 2010 (hereafter referred to as $hus_0$). On 1 April 2010, the specific humidity field displays high values south of the ITD (around $12^\circ$N), within the monsoon flow, and much lower values north of the ITD. At Agoufou, located north of the ITD on 1 April, the specific humidity remains low, around $1\,g/kg$, which is close to its dry season average. The humidity radiative effect associated with the increase of $\epsilon_a$ during the heatwave is therefore discarded in this simulation, whose results are shown in blue in Figure 13.

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$LW_{in}$ and $T_{2m}$ are very close to their values in the reference simulation until DOY 103.

Afterwards, during the heatwave, the two simulations diverge. In the constant moisture simulation, little change in the diurnal fluctuations before and after DOY 103 is simulated, at least until DOY 115 (Figure 13). Overall, daily maxima are close to the reference SARAWI simulation, but the nighttime characteristics of the heatwave period are not reproduced in the constant moisture simulation; $LW_{in}$ and $T_{min}$ remain significantly lower, which reveals the strong sensitivity of the system to the specific humidity.

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The temperature variation due to the Humidity Radiative Effect is further quantified with: $\Delta T_{min}^{HRE} = T_{min} - T_{min}^{hus0}$ where $T_{min}^{hus0}$ is the value of $T_{min}$ in the constant humidity simulation. Similarly, we define $\Delta LW_{in}^{HRE} = LW_{in} - LW_{in}^{hus0}$ for quantifying the HRE on the incoming longwave flux. At Agoufou, the averaged $\Delta LW_{in}^{HRE}$ during the heatwave reaches $59\,W/m^2$, associated with an averaged $\Delta T_{min}^{HRE}$ of $4.75^\circ C$, that reaches values higher than $6.5^\circ C$ between DOY 105 and 109.

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When compared to the observed estimates of longwave CRE and ARE (Figure 5) which are respectively of $15\,m$ and $19\,m^2$ on average during the heatwave at Agoufou, the current estimate emphasizes that HRE stands as the dominant driver of the nighttime warming. According to those estimations, HRE explains 64% of the total radiative warming during the heatwave, while ARE explains 20% and CRE 16%, and HRE leads to a nighttime increase of $2m$-temperature up to $6.5^\circ C$, at Agoufou.

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## 6.4 Maps of the HRE over North Africa

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The spatial structure of $\Delta LW_{in}^{HRE}$ and $\Delta T_{HRE}$ is shown in Figure 14a,b for the 15 April 2010 at 06 UTC, together with the specific humidity field (Figure 14d) and the difference between specific humidity on 15 April 2010 and the constant specific humidity field prescribed in the
<figure><img src="image_14.png" /><figcaption>**Fig. 13** Time series at Agoufou for April 2010 of: $LW_{in}$ (a), $T_{2m}$ (b), $T_{max}$ (c, dashed lines) and $T_{min}$ (c, full lines). Black: CNRM-AM. Red: SARAWI reference simulation. Blue: SARAWI simulation with constant humidity. Orange: clear-sky $LW_{in}$ computed by CNRM-AM. Blue dots at the bottom of panels: cloud cover in CNRM-AM.</figcaption></figure>

constant moisture simulation (Figure 14c). The location of the ITD (here defined as the line of constant h$_{s}$ equal to 8g/kg) is indicated with the white line.

$\Delta LW_{in}^{HRE}$ reaches strong values, up to 100W/m$^2$ south of the ITD, leading to $\Delta T_{HRE}$ up to 13°C. In Figure 14, this strong HRE warming south of the ITD is associated with the northward progression of the monsoon flow in the previous days, and accounts for a specific humidity increase of about 10g/kg (Figure 14c).
<figure><img src="image_15.png" /><figcaption>**Fig. 14** $\Delta LW_{in}^{HRE}$ (a), $\Delta T_{HRE}$ (b), $hus - hus_0$ (c), $hus$ (d) given by SARAWI on 15 April 2010, ie doy 105 (see text for definitions). White line: ITD, defined with $hus = 8g/kg$.</figcaption></figure>

Over the Sahara and other areas north of the ITD, the high values of $\Delta LW_{in}^{HRE}$ and $\Delta T_{HRE}$ are associated with the tropical plume, which also enhances low-level humidity and reaches about $5^\circ C$ (Figure 14c,d).

Figure 14 also underlines that the western Sahel (west to $0^\circ E$) is more affected by HRE than the eastern Sahel (east to $0^\circ E$), consistently with an ITD that does not reach eastern Sahel in April 2010 (Figure 14d). The processes affecting the western and eastern Sahel are therefore distinct, which partly explains why $T_{min}$ were lower in Eastern Sahel (Figure 7). However, HRE affects Nigeria and areas located to the east of $0^\circ E$ but south of $12^\circ N$, which could also partly explains why $T_{min}$ are high in this area (Figure 7g,h).

## 6.5 Can we explain the observed $LW_{in}$ anomalies with the SARAWI HRE estimate ?

On average over the Sahel and Sahara, $\Delta LW_{in}^{HRE}$ reaches high values. Since HRE is caused by moisture which is anomalously high in April 2010 over the Sahel and Sahara (Figure 6e,f), here we analyze whether the observed anomalies of $LW_{in}$ that were explained neither by CRE nor ARE anomalies (section 4) can be better explained by HRE.

The HRE longwave anomaly $HRE^{ano}$ is computed by assuming that the $LW_{in}$ climatological anomaly on DOY 91 (1 April 2010) is the sum of the longwave CRE, ARE and HRE anomalies. Then, we compute $HRE^{ano} = \Delta LW_{in}^{HRE} + HRE_0^{ano}$, with $HRE_0^{ano}$ being the HRE anomaly on 1 April.
<figure><img src="image_16.png" /><figcaption>**Fig. 15** April 2010 time series of anomalies of: $LW_{in}$ (black), longwave CRE (blue), longwave ARE (red) observed by CERES, longwave HRE computed by SARAWI (light blue) longwave CRE+ARE+HRE (orange); averaged over the Sahara (c), the western Sahel (west to 0°, b), the eastern Sahel (east to 0°, c).</figcaption></figure>

Figure 15 shows the April 2010 time series of longwave $HRE^{ano}$ anomalies (light blue), together with the $LW_{in}$ anomalies (black), longwave CRE (blue) and longwave ARE anomalies (red) observed with CERES, as well as the sum of the longwave anomalies CRE+ARE+HRE (orange), averaged over three areas: the Sahara (a), the western Sahel (b) and the eastern Sahel (c).

First, the order of magnitude of $HRE^{ano}$ successfully matches that of the $LW_{in}$ anomalies, particularly over the Sahara and the western Sahel. Secondly, when SARAWI estimates of HRE anomalies are added with CRE and ARE anomalies from CERES (orange curves), the
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resulting time series follows rather closely the observed *LW*<sub>in</sub> anomalies (black), over the
Sahara and the western Sahel.

This result suggests that in the Sahara, the strong positive anomaly of LW<sub>in</sub>, which was
not related to cloud or aerosol anomalies between DOY 100 and 120 is largely explained
by the evolution of the HRE induced by the low-level advection of humidity operated by
the tropical plume event (Figure 15a). In the western Sahel (Figure 15b), this HRE also
explains a major part of the observed anomaly, and is related to a northward penetration of
the monsoon flow.

In the eastern Sahel, which is more affected by aerosols due to a strong dust episode after
DOY 105, HRE remains weaker before DOY 105 (Figure 15c). It increases later, when the
ITD migrates northward in the eastern Sahel, and can explain the increase of LW<sub>in</sub> anomalies
in late April. However, in this area, the high anomaly of LW<sub>in</sub> between DOY 100 and 107
is neither explained by clouds or aerosols nor by humidity radiative effects, which suggests
the possible influence of other physical processes (complex radiative interactions that arise
from overlapping between different types of aerosols and clouds; radiative influence of other
greenhouse gases,...). In addition, the low number of in-situ observations assimilated in the
reanalysis over Eastern Sahel may also play some role.

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7 Discussion and conclusion

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North Africa experienced a major heatwave in April 2010. The present study investigated physical processes acting during this event, using high frequency ground data (AMMA-CATCH), long-term gridded daily temperatures (BEST), satellite-based observations (CERES), climate model simulations (CNRM-AM), and a new soil-surface air layer prognostic model (SARAWI).

During spring 2010, very high daily minimum and maximum temperatures were ob-
served North of 14°N, over large parts of the Sahel and Sahara, together with strong positive
anomalies of LW<sub>in</sub> and negative anomalies of SW<sub>in</sub> at the surface, as well as strong positive
anomalies of AOD, cloud cover and PW. The cloud cover and PW anomalies are associ-
ated with two distinct synoptic events (a tropical plume that reached the northern Sahara
and a northward penetration of the monsoon flow in western Sahel), while the strong AOD
anomaly that prevails during this period is centered on central Sahel.

The heatwave (identified with the methodology of Barbier et al. [2018]) lasts from 10 to 25 April 2010 and is particularly severe at night. Strong positive correlations are found between PW, T<sub>min</sub> and LW<sub>in</sub>, both in space and time, in the areas affected by the heatwave.

Satellite estimates show that, during the heatwave, Aerosol Radiative Effects (ARE) is stronger than Cloud Radiative Effects (CRE) by about +30W/m² for SW<sub>in</sub>, and +15W/m² for LW<sub>in</sub> over both the Sahel and the Sahara. The strong negative anomaly of SW<sub>in</sub> is almost entirely explained by CRE over the Sahara, while it involves a combination of both CRE and ARE, over the Sahel. In contrast, the strong positive anomaly of LW<sub>in</sub> (about +30W/m² over both the Sahara and Sahel) is much higher than longwave CRE or ARE anomalies, which means that neither the cloud cover nor the AOD can explain the observed anomalies of incoming longwave fluxes. The strong correlation between observed LW<sub>in</sub> and PW anomalies points to the significance of a Humidity Radiative Effect (HRE), and this question is further explored with a climate model and a conceptual soil-atmospheric surface layer model.

In order to capture the chronology of the heatwave (and thus helps in performing rele-
vant quantitative comparisons with observations, down to sub-daily time scales [Diallo et al.,
2017]), the dynamics of the climate-model simulation is nudged towards the ERA-interim
meteorological reanalysis. We show that the CNRM-AM simulation faithfully reproduces the Saharan tropical plume event and the Sahelian monsoon surge, as well as the spatial patterns of surface incoming fluxes and temperatures observed during the heatwave. It exhibits systematic biases though, such as too low $LW_{in}$, $LW_{net}$ and $T_{min}$. Those shortcomings do not affect the ability of the model to represent the sharp transition between the pre-heatwave and heatwave regime, closely associated with the arrival of the monsoon flow in the Sahel, whose main observed characteristics are well-reproduced. The pre-heatwave regime is dry with low nighttime temperatures, low $LW_{in}$ and $LW_{net}$ fluxes, and high Diurnal Temperature Range (DTR); while the heatwave regime is moister with higher nighttime temperatures, stronger $LW_{in}$ and weaker DTR, both in observations and simulations.

In the CNRM-AM simulation, the nocturnal cooling of the atmospheric surface layer is almost entirely due to longwave radiative transfer, whereas daytime evolution of the surface-layer air temperature results mainly from the combination of two dominant processes: long-wave radiation and turbulence. During the heatwave, nighttime air cooling by longwave radiation is lower. Similarly, the nighttime soil cooling is lower, because $LW_{in}$ increases more than $LW_{up}$. The combination results in a stronger thermal coupling between the soil and the atmospheric surface layer. The increase of $LW_{in}$ is strongly correlated with the increase in humidity on areas where the monsoon flow (Western Sahel) or the tropical plume (Sahara) moistens the environment.

The new conceptual model SARAWI (cf section 2.5) is used to explore further the radiative greenhouse effect of water vapor. We show that, at first order, regional-scale processes can be decoupled from local physics, namely turbulence and longwave radiative transfer between the soil and the atmospheric surface layer. By prescribing the former (here from the CNRM-AM simulation) and explicitly and prognostically computing the impact of the latter on temperatures, we are able to reproduce with a very good accuracy the surface energy budget, the radiative and turbulent warming of the atmospheric surface layer, $LW_{in}$ fluxes, soil and air temperatures, and their diurnal cycles given by CNRM-AM. Unlike a complex 3D GCM, SARAWI is well-suited to perform and interpret sensitivity tests in simple and unambiguous ways. In the present study, it allows us to highlight the crucial impact of water vapor during the heatwave. Over the Sahel, the greenhouse effect of water vapor enhances $LW_{in}$ and $T_{min}$ up to 100W/m² and 13°C respectively.

In addition, a quantitative analysis shows that the sum of the HRE anomaly estimated using SARAWI, with the weaker CRE and ARE anomalies from CERES, explain the evolution of the observed $LW_{in}$ anomaly over the Sahara and the western Sahel. This demonstrates that the increase of air emissivity due to the increase of moisture is the dominant driver of the heatwave nighttime temperatures; and that the severity of this heatwave can be explained by the increased greenhouse effect of water vapor.

In summary, our study provides insights into the interactions arising between processes operating at different scales: during the April 2010 heatwave, the synoptic-scale advection of warm air is negligible. However, the synoptic-scale advection of water vapor (associated with either the monsoon flow or the tropical plume) emerges as a fundamental driver. Indeed, the evolution of surface fluxes, soil and surface air temperatures are almost entirely explained by physical processes, among which longwave radiative transfers, which are very sensitive to water vapor variations.

Beyond this particular case study, a simplified model such as SARAWI can be useful for carrying sensitivity experiments at very low computation cost; e.g. for the implementation of new physical parameterizations. More broadly, such a modeling approach could also be useful for comparing the physical mechanisms operating in different climate models. This
926

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928

may be particularly relevant here given the importance of physical processes involved in land-atmosphere interactions on the climate during this period of the year.

Finally, this study further raises several open questions:

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935

936

937

938

939

940

941

942

943

944

945

946

947

948

- Physical processes and mechanisms driving nighttime temperatures have been highlighted, but the evolution of $T_{max}$ during this heatwave appeared complex, and seems to imply a balance between physical processes. To what extent do cloud, aerosol or humidity shortwave radiative effects lowers $T_{max}$? To what extent can a heat accumulation phenomenon in the upper boundary-layer as described by Miralles et al. [2014] warm the low-layers during daytime via the afternoon convective and turbulent mixing?

- Could other processes involving larger-scale circulations, as recently highlighted in mid latitudes by Zschenderlein et al. [2019] play a role? In particular for the Sahel, to what extent and how are tropical waves influencing Sahelian heatwave occurrence and characteristics? At relatively smaller scale, are convectively generated cold pools (which can advect water vapor up to the Sahara, [Garcia-Carreras et al., 2013]) playing a role during spring sahelian heatwaves?

- Barbier et al. [2018] show that there is a strong climatologic nighttime warming trend during heatwaves. To what extent can this trend be related to a climatic increase of atmospheric water vapor content [IPCC, 2013], especially over the Saharan region [Evan et al., 2015]? And how would this affect wet-bulb temperature which stands as an important variable with respect to heath considerations (e.g. [Sherwood and Huber, 2010])?

- Finally, can this link between water vapor and $T_{min}$ help to analyze climate projections and reduce uncertainties on extreme weather frequency and severity for the coming century?

949

## A Appendix : Configuration of the SARAWI simulations and tuned coefficients

950

951

952

In the SARAWI simulations used in the present study, physiographic and physical parameters are statistically tuned using the monthly-average values resolved by CNRM-AM. We also differentiate nighttime and daytime conditions when the considered parameter physically depends on static stability. This leads to:

953

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956

957

$\epsilon_a$: Coefficients $a_i$ of equation 9 are estimated using longwave fluxes simulated by CNRM-AM which are regressed with the atmospheric specific humidity and air temperature. We can consider $a_i$ coefficients obtained from a regression that include all points in North Africa, or alternatively use $a_i$ coefficients which vary depending on the climate zone (Sahara, Sahel, Guinea). Both approaches lead to similar results (with a 5.3 W/m$^2$ or 1.3% uncertainty on $LW_{in}$ and a 0.28°C uncertainty on $T_{2m}$). A regional fitting over North Africa gives $a_1 = 0.667$, $a_2 = 1.17 \times 10^{-2}$ with hus in g/kg and $a_3 = 4.55 \times 10^{-4}$ with $T_a$ in °C.

959

960

961

962

$\epsilon_s$: As for $\epsilon_a$, we use CNRM-AM longwave fluxes to estimate $\epsilon_s$ (which uses the ECOCLIMAP database, [Champeaux et al., 2005; Faroux et al., 2013]). It is almost constant and equal to 0.9946 ± 0.0065 over all North Africa in CNRM-AM. We take this mean-value as a constant for all continental grid points (this leads to a 0.11 W/m$^2$ or 0.03% uncertainty on $LW_{in}$ and a 0.08°C uncertainty on $T_{2m}$ as compared to the local value for each grid point).

964

965

966

967

$C_s$: In order to correctly fit $C_s$, we use equation (2) with the resolved fluxes and temperatures given by CNRM-AM, which takes its soil physiographic characteristics from the ECOCLIMAP database [Champeaux et al., 2005; Faroux et al., 2013]. We average the different terms for each grid point separately over daytime and nighttime, from which we estimate two physiographic 2D fields $C_s^{night}(lon, lat)$ and $C_s^{day}(lon, lat)$.
968 $h_{rad}$: We compute $h_{rad} = c_{rad} \cdot \delta z$ at each grid point by determining the value of $h_{rad}$ that minimizes the root mean square error between the CNRM-AM values of $\frac{\partial T_a}{\partial t}$ and the estimated values of that tendency according to equation (6). Results show that the value of $c_{rad}$ is very homogeneous over all continental North Africa, so we choose to keep one constant value in SARAWI equal to the average over the continental area : $h_{rad} = 4.74 \cdot \delta z$. Physically, $h_{rad}$ corresponds to a characteristic penetration depth of the upwelling longwave flux emitted by the surface, or alternatively to the depth of the layer radiatively warmed (or cooled) by the surface.
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973
974

975 $h_{turb}$: It is fixed equal to the height between the first and the second layers of the CNRM-AM simulation (35m).
976

977 $c_{t2m}$: The parameterization available in CNRM-AM [Mahfouf et al., 1995] is used here to prescribe $c_{t2m}$, in order to facilitate comparison with the diagnosed $T_{2m}$ in CNRM-AM simulation.
978

979 $C_h$, $K_s$, $K_h$: In coupled soil-atmospheric models, the drag coefficient $C_h$ usually depends on the static stability (see Noilhan and Mahfouf [1996] for the ISBA model used in CNRM-AM). Similarly, the turbulent diffusivity in low-layers also strongly varies with the static stability (e.g. [Yasuda, 1988; Largeron et al., 2010]).
980
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982
983 Here, we choose to use constant daytime values: $C_h = 4 \cdot 10^{-3}$, $K_s = 1.6 \cdot 10^{-4}$, $K_h = 0.94 \ m^2 \cdot s^{-1}$; and constant nighttime values about 8 times lower: $C_h = 5 \cdot 10^{-4}$, $K_s = 2 \cdot 10^{-5}$, $K_h = 0.08 \ m^2 \cdot s^{-1}$. Values are tuned to recover the heat fluxes given by the CNRM-AM simulation.
984
985

986 **Acknowledgements** This work has been done in the framework of the ACASIS project from the French national research agency (ANR). The authors acknowledge support from ANR ACASIS, grant ANR-13-487 SENV-0007. Authors also acknowledge NASA for the dissemination of the CERES satellite products through the website https://ceres.larc.nasa.gov/, the Berkeley Earth for their open global temperature database (berkeleyearth.org/), and the scientists and technicians who collected the AMMA-CATCH data in the Sahel. They also thank Mireille Tomasini for usefull discussions on heat budget analysis, and Clara Theeten for her carefull proofreadings of the present paper.
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