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Mapping past, present and future dew and rain water resources for biocrust evolution in southern Africa

Mapping past, present and future dew and rain water resources for biocrust evolution in southern... J. Hydrol. Hydromech., 69, 2021, 4, 400–420 ©2021. This is an open access article distributed DOI: 10.2478/johh-2021-0030 under the Creative Commons Attribution ISSN 1338-4333 NonCommercial-NoDerivatives 4.0 License Mapping past, present and future dew and rain water resources for biocrust evolution in southern Africa 1, 2 2, 3* Marc Muselli , Daniel Beysens Università di Corsica Pasquale Paoli, Avenue du 9 septembre, BP 52, 20250 Corte, France. OPUR, 2 rue Verderet, 75016 Paris, France. Physique et Mécanique des Milieux Hétérogènes, CNRS, ESPCI Paris - PSL University, Sorbonne Université, Sorbonne Paris Cité, 10 rue Vauquelin, 75005 Paris, France. Corresponding author. Tel.: +33(0)689864717. E-mail: daniel.beysens@espci.fr Abstract: Biocrust sustainability relies on dew and rain availability. A study of dew and rain resources in amplitude and frequency and their evolution is presented from year 2001 to 2020 in southern Africa (Namibia, Botswana, South Africa) where many biocrust sites have been identified. The evaluation of dew is made from a classical energy balance model using meteorological data collected in 18 stations, where are also collected rain data. One observes a strong correlation between the frequency of dew and rain and the corresponding amplitudes. There is a general tendency to see a decrease in dew yield and dew frequency with increasing distance from the oceans, located west, east and south, due to decreasing RH, with a relative minimum in the desert of Kalahari (Namibia). Rain amplitude and frequency decreases when going to west and north. Short-term dew/rain correlation shows that largest dew yields clearly occur during about three days after rainfall, particularly in the sites where humidity is less. The evolution in the period corresponds to a decrease of rain precipitations and frequency, chiefly after 2010, an effect which has been cyclic since now. The effect is more noticeable towards north. An increase of dew yield and frequency is observed, mainly in north and south-east. It results in an increase of the dew contribution with respect to rain, especially after 2010. As no drastic changes in the distribution of biomass of biocrusts have been reported in this period, it is likely that dew should compensate for the decrease in rain precipitation. Since the growth of biocrust is related to dew and rain amplitude and frequency, future evolution should be characterized by either the rain cycle or, due to global change, an acceleration of the present tendency, with more dew and less rainfalls. Keywords: Biocrust; Dew and rain evolution; Dew/rain ratio; Dew/rain correlation; Southern Africa; Climate change. 1 INTRODUCTION enhanced effect between dew and artificially revegetation ecosystems in the arid desert ecosystem in Shapotou (China). Li Biocrust are typically found in drylands with arid or semi- et al. (2021a, b), in recent papers, determine that biocrust arid ecosystems. In great interaction with the soil, biocrust benefits from non-rainfall water deposition and modify their concern cyanobacteria, lichens, algae and mosses. These organ- distribution in drylands soils. Dewfall can be presented as a isms contribute strongly in the ecosystem’s functioning and critical source of water in deserts environments allowing to plant organization and are present all around the world. determine the sustainability of sand to stabilize planted Numerous works detail their physical, chemical and biologi- vegetation (Zhuang and Zhao, 2017). Dew, fog and rain can cal characteristics in semi-arid or arid climates. Negev (Jacobs play an important role for the development of biocrust in semi- et al., 2002; Kidron and Tal, 2012), Europe (Raggio et al., arid regions. Kidron (2019) suspects dew to be a necessary 2021), Spain (Cano-Díaz et al., 2018), China (Yao et al., 2019), water source for cyanobacteria. Biocrust alter non-rainfall USA (Aguirre-Gutiérrez et al., 2019) are a few examples. distribution by depth, concentrating it in the surface (Li et al., According to Chen et al. (2020), biocrust correspond to 30% of 2021a, b). Biocrust can boost the use of non-rainfall water global drylands. It is in China, Australia, North America and according to Ouyang et al. (2017). Büdel et al. (2009) conclude Spain in Europe that are found the more studied biocrust sites. their study by noting that the time frequency of rain In the present study, a representative area for biocrust studies precipitations is more important than their amount. was chosen in a less investigated area, the southern part of The amount and frequency of rain and dew are then the main Africa. Namibia, South Africa and Bostwana are the main factors which influence the growth of biocrust. This paper aims countries involved in this study, representing 18 sites of meas- to evaluate the evolution of these contributions to over a long urement (7 in Namibia, 7 in South Africa and 4 in Bostwana, period of time (20 years, from 2001 to 2020) in order to put in respectively). One should note that these locations are based on evidence the long term trend and extrapolate to the near future. previous works of a few scholars within certain research sites Because certain data are lacking before 2011, a few analyses and cannot obviously replace an objective map. A map of soil are restricted to 10 years (2011–2020). can help to locate biocrust, it is given in Fig. 1 together with the The paper is organized as follows. After having reported on above studied sites. measurements and methods in Section 2, mainly concerning the Moisture from atmosphere (rainfall, fog, dew, vapor physical model used to determine the dew yields, Section 3 absorption) plays an important role in sustaining life in arid or is devoted to the main results with maps i) for dew and rain at- semi-arid climates. Pan et al. (2010) concluded on the mutual mospheric deposition, ii) cumulative rainfall and dew yields 400 Mapping past, present and future dew and rain water resources for biocrust evolution in southern Africa comparisons and iii) short time and longtime evolution of dew Namibia (824 292 km² surface area). The country shows and rainfalls yield and frequency. A Section 4 is devoted to dis- three different climates, the most prevalent being semi-arid cussions and relation of the rain and dew studies with biocrust. (Köppen-Geiger classification BSh) and hot desert (BWh). The less frequent is cold desert climates (BWk). The climate is characterized by great differences in day and nighttime temper- 2 METEOROLOGICAL DATA AND METHODS atures, low rainfall and overall low humidity. Along the coast, 2.1 Dew yield estimation from meteorological data the average annual precipitation does not exceed 15 mm. Inside the country, the continental plateau has a more contrasted situa- In order to estimate the dew potential, Beysens (2016) tion with abundant precipitations (> 500 mm). The dry season, developed an energy balance model which, thanks to some between May to October, correspond to little or no rainfall approximation, uses only a few classical meteorological data during July and August. Wildlife uses mainly waterholes and without adjustable parameters: cloud cover (N, oktas), wind −1 rivers when the water sources dry up. In desert areas, the aver- speed (V, m s ), air temperature (T , °C), air relative humidity age minimum temperature is cold and can fall below freezing at (RH, %) and dew point temperature (T , °C). Near the ground night. The wet season, between November to April, present level where dew forms, in the atmospheric boundary layer, the daytime temperatures of about 30 °C with the first rains ob- contribution from water vapor (about 0.2–2% by volume) and, served in November (mean rainfall 26 mm to a maximum in to a lower extent, carbon dioxide (about 0.03% in volume) is of January with 91 mm). Sometimes, torrential downpours are great importance for the radiative balance, with radiation from observed in the afternoon up to March and April, where rainfall water vapor being by far the more important of the two. The –1 decrease and stops before the dry season. results are concerned with dew yields h [mm (Δt) ] where Δt Botswana (581 730 km² surface area). The climate is charac- corresponds to the period (in hours) of the analyzed data. It is terized as hot semi-arid, the dominant climate (Köppen-Geiger assumed that the substrate emissivity is unity (which is close to classification BSh), and hot desert (BWh). During summer the emissivity ≈ 0.98 of a wet substrate, see Trosseille et al., months (November–March), a rainy season is observed with 2021) and is thermally insulated from below. The data can be high temperatures. The mean annual rainfall varies from over obtained from the airport meteo stations by using the following 650 mm in the extreme northeast area (Chobe District) to a formulation: minimum of 250 mm in the extreme southwest part (Kgalagadi District). The winter season during May to August corresponds Δt  hH=+ LRE (1) ()  to the dry season with less than 10% of the annual rainfall. The  variability of rainfall increases while the quantity decreases toward the south and west. The factor Δt is the measurement period of the data (here 6, South Africa (1.22 million km² surface area). The country 3 or 1 h. depending on the stations). The data for h > 0 corre- corresponds to a subtropical area, influenced by the vicinity of spond to condensation and h < 0 to evaporation, which have to the oceans along the coastlines and the altitude of interior be discarded. The quantity HL represents the convective heat plateau (1 500 m in the dolerite-capped Roggeveld scarp in the losses between air and condenser, with a cut-off for windspeed south-west, to a height of 3 482 m in the KwaZulu-Natal Dra- −1 V > V0 = 4.4 m s where condensation vanishes: kensberg). The country has several climatic zones depending on its geography: in the northwest, near the Atlantic coast stretch-  Δt  ing to the center of the country, the climate is mainly character-  0.06 TT−+RE ifV <V ()  da 0  h = 12 (2)  ized by arid lime (BWh) or cold (BWk) deserts. In the south-east, the country offers a temperate climate with dry and 0 if V >V  0 hot (Csa) or warm (Csb) summers. Finally, along the southern coast of the country, one finds a hot (BSh) or cold (BSk) arid The quantity RE is the available radiative energy, which de- climate with steppes but also a temperate zone, along the ocean pends on air water content (measured by the dew point tem- between the towns of George and Port Elisabeth with dry perature Td, in °C), site elevation H (in km) and cloud cover N winters and hot summers (Cwa). The eastern part of the coun- (in oktas): try, which is more mountainous, is characterized by a predomi- nantly temperate climate, without a dry season, with hot to  1+− 0.204323HH 0.0238893 −  RE=× 0.37 temperate (Cfb) or cold (Cfc) summers. Mean rainfall is about 23 −  18.0132 −+ 1.04963HH 0.21891 ×10T () d 460 mm with a large dispersion according to the location.  Usually, the western Cape presents major rainfalls in winter T + 273.15 N  d whereas the rest of the country exhibits summer rainfalls. ×− 1   285 8 The spatial distribution of rainfall between Namibia,   Bostwana and South Africa presents some differences in space (3) and time (New et al., 2000). In Namibia, for the locations of By filtering the rain and fog events and integrating the time Dante Cave at the north of the country, summer rainfall is ob- series on a daily time-step corresponding to h > 0, calculated served from October to April, with mean annual rainfall be- daily yields and their cumulated values are obtained. We give –1 tween 500 and 600 mm yr , a value much less than the poten- –1 an example of calculation in Appendix 1. tial evapotranspiration estimated to 2900 mm yr (Railsback et al., 2019). A similar behavior is observed at the frontier be- 2.2 Studied area tween Bostwana and South Africa (27°S, 21°E), with summer rainfall. The situation is more complex in South Africa. Ac- The study area (Fig. 1) is characterized by a spatial extent of cording to the location, one observes winter rainfall as in Cape about 3 000 000 km between 15° to 35° south latitude and 13° Town with precipitations mainly during April to September, weak precipitations but year-round in George and summer to 30° for east longitude. In the following are detailed the dif- rainfall with a dry winter in Pretoria (Railsback et al., 2019). ferent climate characteristics of the countries. 401 Marc Muselli, Daniel Beysens Fig. 1. Map of soils in the studied area (from Jones et al., 2013). Black rectangle and black letters are airport stations. The interrupted blue rectangle corresponds to the biocrust sites (green circles, see Chen et al., 2020). Table 1. Sites where atmospheric data are collected (7 stations in Namibia, 4 stations in Bostwana and 7 stations in South Africa). They are sorted according to their longitude (west to east). The sky condition data availability (% of the total sky conditions data) is reported for each station. Country Site Abbreviations Latitude Longitude Altitude Distance to data Sky conditions Name (m asl) the sea (km) period data (%) Namibia Swakopmund SM 22° 40' 0'' S 14° 34' 0'' E 61 8 2010-2020 52.4 Namibia Walvis Bay WB 22° 58′ 47″ S 14° 38′ 43″ E 86 14 2010-2020 52.4 Namibia Luderitz L 26° 41′ 15″ S 15° 14′ 34″ E 131 1 2006-2020 0.0 Namibia Ondangwa OD 17° 52′ 41″ S 15° 57′ 09″ E 1099 385 2011-2020 47.7 Namibia Oranjemund OJ 28° 35′ 05″ S 16° 26′ 48″ E 5 6 2005-2020 0.0 Namibia Eros E 22° 36′ 44″ S 17° 04′ 50″ E 1699 266 2011-2020 45.2 Namibia Keetmanshoop K 26° 32' 13'' S 18° 06′ 40″ E 1069 285 2011-2020 40.0 South Africa Cape Town C 33° 58′ 10″ S 18° 35′ 50″ E 46 3 2001-2020 100.0 South Africa Upington U 28° 24′ 04″ S 21° 15′ 35″ E 844 432 2001-2020 77.3 Botswana Shakawe SK 18° 22′ 25″ S 21°50′ 00″ E 1008 895 2005-2020 100.0 South Africa George G 34° 0' 20'' S 22° 22' 42'' E 197 7 2001-2020 89.9 Botswana Maun MN 19° 59' 0'' S 23° 26' 0'' E 945 1106 2001-2020 100.0 South Africa Mahikeng MK 25° 48' 27"S 25° 32' 40" E 1274 680 2001-2020 65.6 South Africa Port Elizabeth P 33° 59' 5'' S 25° 37' 2'' E 68 3 2001-2020 100.0 Botswana Gaborone GB 24° 33′ 19″ S 25° 55′ 06″ E 1006 695 2001-2020 99.9 South Africa Bram Fischer B 29° 05′ 38″ S 26° 18′ 14″ E 1349 418 2001-2020 76.1 Botswana Francistown F 21° 10' 0'' S 27° 29' 0'' E 1002 726 2002-2020 100.0 South Africa Wonderboom W 25° 39′ 13″ S 28° 13′ 27″ E 1240 460 2005-2020 88.6 2.3 Extraction data 0.1 m in flat areas) where V = 0. Available data were extracted from the online data base “Weather Underground” (Weather All ground stations are installed on international or national Underground database, 2021) during a period of maximum 20 airports where standard meteorological parameters are meas- years (2001–2020) with a minimum of 10 years (2011–2020) ured. The meteorological stations meet the data measurement depending on data availability (Table 1). standards of the World Meteorological Organization. Air T Dew yields have been computed from Eq. (2) using the (°C) and dew T (°C) temperatures, relative humidity (RH, %), above standard meteorological databases extracting air and dew atmospheric pressure (P, Pa) are measured in a meteorological point temperatures (T and T , °C), relative humidity (RH, %), a d –1 –1 −1 shelter, 1.5 m from the ground. The windspeed (V, km h ) and wind speed (km h to be transformed in m s ), wind direction direction (sectors or degrees) are measured at 10 m from the (sectors), absolute pressure (hPa) and sky cover. An hourly ground. Note that wind speed can be extrapolated at any height time-step for measured data is accessible except for Oran- z above the ground by the classical logarithmic variation (see jemund and Luderitz (Namibia) where two time-steps are avail- able (Oranjemund: 6 h on 2005–2014 and 3 h on 2014–2020);    z 10 Vz =V ln / ln e.g. Pal Arya, 1988) () where V10 is    Luderitz (6 h on 2006–2012 and 3 h on 2012–2020). zz cc  Wind direction values in degrees have been computed from windspeed at 10 m and z is the roughness length (generally ≈ wind direction sectors (N, NNE, NE, E, ESE, SE, S, etc.) using 402 Mapping past, present and future dew and rain water resources for biocrust evolution in southern Africa a standard law of proportionality: 0° for north, 180° for south itz, Swakopmund and Oranjemund) benefit from high dew –1 and calculation of all intermediate values with respect to these yields (> 10 mm yr ) mainly explained by the high humidity references. due to the vicinity of the Atlantic Ocean. For example, mean –1 The sky cover was considered variable if it varies by one or dew yields in the range 12.6 to 38.2 mm yr (for N = 0, 1, missing more of the reported values (CLR, FEW, SCT, BKN, or OVC) 3) have been obtained in Swakopmund and Walvis Bay, located during the period of observation (NOAA’s national weather near the Namib national Park, corresponding to mean monthly service glossary, 2021). Cloud cover in oktas was computed dew yields between 2.8 and 6.9 mm. For both stations, dewy from the nightly observation of sky cover using the correspond- days represent between 79.1 (Swakopmund, N = 3) and 85.8% ence listed in Table SM2 in Supplementary Materials, which (Walvis Bay, N = 0) of the year. On the other hand, the stations was used in a previous work (Muselli et al., 2020). However, established in the interior of the country suffer from very low –1 cloud cover is sometimes not available at night on some sites annual dew yield (< 5 mm yr ). For example, Eros, Keetmans- (the missing percentage of total values is noted for each site in hoop and Ondangwa, respectively located at about 250 and Table 1). When the sky conditions data are unavailable, we 350 km from the ocean, exhibit annual dew yields less than imposed to these sites three possible values, corresponding to 4.9 mm. In Keetmanshoop, monthly dew yields are very weak the most probable: N = 0, 1 and 3. with a mean of 0.1–0.3 mm and a monthly maximum of up to Measured rainfall data, available on a daily time step, are 1.8 mm. For Eros and Keetmanshoop, only 10–20% of the days extracted from the meteorological data base (Infoclimat data- are dewy (min = 8.7% and max = 18.4%), while for Ondangwa base, 2021). All data are obtained for the same stations as used it is 25% or even 15% (N = 0 for missing data) or even one for dew calculation except for Swakopmund where the rainfall day a week in the most unfavorable case (N = 3 for missing data of Walvis Bay are used (both sites are only 25 km apart). data). The situation is more homogeneous in Botswana. The mean 2.4 Kriging maps annual dew yields are between 6.9 and 16.2 mm depending on the sites (annual dew yield min = 1.8–6.6 mm and max = 16.5– Kriging methodologies are mainly used for mapping spatial 26 mm), with monthly yields averaging between 0.6 and 1.4 distribution of a given variable. The classical algorithm is pre- mm (min = 0 mm and max = 4.2–5.9 mm). sented in Appendix 2. Belkiri et al. (2020) use Kriging to study Except in Upington (mean < 5.5 mm), located in the north- ground water composition. Tomaszkiewicz et al. (2016) pro- ern Cape Province of South Africa on the banks of the Orange pose ordinary Kriging to develop dew maps integrating project- River, and Mahikeng, near to the Bostwana frontier (mean < ed climate changes in the Mediterranean basin. Martinez et al. 9.8 mm), all the South Africa country exhibits mean annual dew (2017) present median polish Kriging (MPK) for space-time yields more than 15 mm. For example, Cape Town, Port Eliza- analysis of monthly precipitation in Colombia. Pue et al. (2021) beth and George cities, on the south coast, or Wonderboom and introduce a Kriging-based Gaussian process for the evaluation Bram Fischer (near respectively Pretoria and Johannesburg), for the prediction of soil water retention in tropical and temper- present averaged annual dew yields of more than 18.3 mm, and ate climates. Other studies combine Kriging models for the up to 27 mm. Whereas the maximum monthly dew yields do not estimation of rainfall with Lagrangian (Amani and Lebel, 1997) exceed 4.7 mm in Upington and Mahikeng, the other cities pre- or Bayesian (Lima et al., 2021) approaches. sent monthly dew yields larger than 4.5 mm, and up to 7.7 mm. The spatial distribution of dew yields was determined by Kriging (Fig. 2, for N = 0, 1, 3 for missing data). Maps of mean 3 RESULTS annual dew yields are presented in (Figs. 2a, b, c). As expected 3.1 Evolution and described in the literature (Henschel et al., 2007; Soder- berg, 2010), dew exhibits the highest yields along the west For each site, dew (subscript i = d) and rain (subscript i = r) coast of Namibia corresponding to the Namib Desert. This monthly yields hi (mean, min, max in mm) are computed. desert represents about 81 000 km² and stretches over 1,500 km Annual dew yield (mm) is deduced by adding the monthly hi: along an 80 to 160 km wide north-south coastal strip along the Atlantic Ocean. One also clearly observes the decrease in yields Hh = ()t (4) ii  inland, especially from the central plateau towards the desert of t =1 Kalahari representing a surface of 900 000 km² with 600 000 km² in Namibia. However, one notes that in these critical areas, In order to estimate the evolution, monthly dew yields can monthly dew yields can reach mean and maximal values up to be fitted by a linear regression on the measured period: 2–3 mm and 6–8 mm, respectively. Note that the biocrust sites are located in regions of moderate dew yield. ht =+ α t h (5) ( ) ii i,0 More generally, there is a tendency to see a decrease in dew yield with increasing distance from the oceans, located W, E With t in month, the coefficient α = dh / dt represents the ii and S. A clear decrease in nocturnal RH from west to east is monthly evolution rate. obvious (Fig. 2d), with the largest dew yields (Fig. 2a, b, c) corresponding to the regions of highest RH. 3.2 Dew yields 3.2.2 Evolution map 2001–2020 3.2.1 Data description In Fig. SM1 (Supplementary Materials) are plotted the evo- Mean, minimum and maximum dew yields are calculated on monthly and yearly time bases and reported in Table SM3 in lution of the summed value of dew yield, sum()hh = dt Supplementary Materials. The calculated annual dew yields dd  show significant variations depending on the sites studied even 0 within the same country (Fig. 2 and Table SM3). on a monthly basis, with t the starting year (see Table 1). The In Namibia, the sites on the west coast (Walvis Bay, Luder- dew rate is either nearly constant during the period 403 Marc Muselli, Daniel Beysens Fig. 2. (a, b, c): Map of annual dew yield Hd (in mm) in the period 2001–2020 corresponding to three scenarios for missing N data (see text and Table 1). (d): Mean nocturnal RH (%) during dew events. Red letters: Meteo sites (see Table 1); circles: Biocrust sites according to Chen et al. (2020); right cross: Gobabeb site studied by Henschel et al. (2007) and Soderberg (2010); inclined cross: Potchefstroom site studied by Baier (1966). N = 0 N = 1 N = 3 Fig. 3. Difference between 2020 and 2011 annual dew yields (mm) for three scenarios corresponding to the missing N data (see text and Table 1). Red letters: Measurement sites (see Table 1); circles: biocrust sites according to Chen et al. (2020); right cross: Gobabeb site studied by Henschel et al. (2007) and Soderberg (2010); inclined cross: Potchefstroom site studied by Baier (1966). (Swakopmund, Walvis Bay, Eros, Keetmanshoop, Cape Town, By considering the period where meteorological data are Port Elizabeth, Gaborone, Bram Fischer) or increases (Luderitz, available on all sites (2011–2020), one can determine the evolu- Oranjemund, Upington, Shakawe, George, Maun, Mahikeng, tion of the average yield at any point in the study area by Wonderboom) after year 2010. One will see in Section 3.3 that subtracting annual dew yields between years 2020 and 2011. the year 2010 is also the year where rainfalls significantly Figure 3 shows the difference Δhd = hd (2020) – hd (2011). One decrease. sees that the evolution is different according to the locations. 404 Mapping past, present and future dew and rain water resources for biocrust evolution in southern Africa –1 Although dew decreases in two places where it was the most but with lower rainfall (285 mm year with a mean of 23.8 –1 abundant (SW and NE to a lesser extent), it increases in the mm month ). NW (Ondangwa, Eros) where dew was the lowest. A noticeable One notes a marked decrease in precipitation during the 20 increase is seen in N (Maun, Shakawe) and SE regions (Bram years period, all sites show α (hr) < –0.2, particularly in Eros Fischer). One notes that the biocrust sites are mostly located in and Ondangwa in Namibia, the 4 cities of Bostwana, and regions of null or moderate dew decrease. George and Bram Fisher in South Africa. Coastal sites in Namibia (Oranjemund, Luderitz, Swakopmund and Walvis 3.3 Rainfall Bay) show a smaller decrease (α (h ) ≈ 0). When looking at 3.3.1 Data description Fig. SM1 in Supplementary Materials (summed values of h ), one realizes that the main change in rainfalls occurred in 2010. Table 2 and Fig. 4 present annual and monthly mean, min It is from this year that a gradual change in rain can be ob- and max rainfall extracted from Infoclimat database (2021) for served. the studied period (sites: See Table 1). From a general point of The rainfall repartition presented in Table 2 is confirmed by view, rain decreases towards W and N. As described below, the Kriging map obtained for the annual mean rainfall (Fig. 4a). cities located at the Namib Desert exhibit lower rain precipita- Rainfall increases markedly from west to east (0–200 mm at the tions: 13.4 mm in Swakopmund and Walvis Bay (i.e. 1% of Atlantic coast to 600 to 700 measured at the south-east of South rainfall events by year) and in a lesser extent, Oranjemund with Africa). The same trend is observed with the monthly mean and a mean annual rainfall of about 42 mm (i.e. 5% of rainfall maximum rainfall volumes (Figs. 4b, c). The monthly average events by year). In these areas, precipitations are very erratic, varies from 0 to 20 mm (W) to 50 to 60 mm (SE). with no rain for several months and few intense precipitations events. In the inland, rainfall is slightly more abundant with 3.3.2 Evolution map annual averages of 115, 189 and 306 mm for Keetmanshoop, Ondangwa and Eros, respectively. Although these areas can By subtracting the precipitation values between years 2020 exhibit months without any rain, the monthly averages are and 2011 one can map (Fig. 5) the difference Δhr = hr (2020)– greater than 10 mm. However, one notes that less than 11% of hr (2011). Although the mean precipitation decreases, the evolu- the days of the year are rainy days (10.9%, 5.3% and 3.7% in tion is different depending on the locations. Rain mainly de- Eros, Ondangwa and Keetmanshoop, respectively). creases in the north regions (Maun, Shakawe, Eros), where dew For Botswana, the situation is more homogenous, with a was seen to increase during the same time period (Fig. 3). A mean rainfall of 463.2 mm observed in the four cities of Gabo- small zone in south west (Cape Town, Oranjemund) exhibits a rone, Maun, Francistown and Shakawe. With one or two precipitation increase. It is worthy to note that the biocrust zones months during the year without rain, this region present mean are mostly in the regions that experienced a decrease in rain. regular monthly rainfall of about 39 mm, with 13.4% of the days being rainy. 3.4 Correlation between dew and rain yields South Africa exhibits a contrasted behavior. The regions lo- cated along the ocean in the south and south east of the country The occurrence of dew is related to the presence of have heavy rainfall with annual amounts greater than 500 mm atmospheric high humidity. Some correlations therefore exist (Mahikeng, Cape Town, George, Port Elizabeth, Bram Fischer, between the frequency and amplitude of rain and the amplitude Wonderboom), with up to 715 mm in George (18–31% of the of dew yields. Two kinds of correlation can occur, a temporal year are rainy days). Monthly averages are important with a correlation, where dew forms after rain events, which have mean of about 49.6 mm (23.5% rainy days in the year). increased the atmosphere RH, and an amplitude correlation. Upington is an exception, located further west of the country, Both correlations are studied in the following. Table 2. Mean, minimum and maximum yearly (Hr) and monthly (hr) rainfall calculated from meteorological from 2001 to 2020 are fitted to Eq. (5) with free parameters α = dh / dt and h . r r r,0 –1 H (mm yr ) h (mm) year r r α h r r,0 Site frequency –1 (mm month ) (mm) Mean Min Max Mean Min Max (%) Swakopmund 13.4 0.0 56.0 1.1 0.0 41.2 –0.005 1.5 0.9 Walvis Bay 13.4 0.0 56.0 1.1 0.0 41.2 –0.005 1.5 0.9 Luderitz 18.6 1.0 83.5 12.4 0.0 64.1 –0.024 3.2 1.8 Ondangwa 189.4 6.6 453.0 15.8 0.0 155.0 –0.283 32.9 5.3 Oranjemund 42.2 7.0 225.8 3.5 0.0 115.6 –0.030 6.4 5.0 Keetmanshoop 115.7 20.8 278.4 9.6 0.0 145.1 –0.044 11.0 3.7 Cape Town 542.1 249.0 888.8 45.2 0.0 238.0 –0.148 57.0 24.8 Upington 285.1 53.0 518.4 23.8 0.0 261.4 –0.167 38.3 10.4 Shakawe 423.5 8.4 1072.3 35.3 0.0 447.1 –0.493 82.8 13.0 George 715.4 333.0 1223.7 59.6 0.0 290.5 –0.260 79.7 30.7 Maun 482.8 20.0 1115.9 40.2 0.0 375.3 –0.468 79.8 14.9 Mahikeng 582.8 182.0 1158.1 48.6 0.0 320.3 –0.135 55.5 19.7 Port Elizabeth 641.8 308.0 1103.8 53.5 0.0 235.5 –0.171 64.2 26.8 Gaborone 464.3 80.2 1023.3 38.7 0.0 372.5 –0.374 68.0 11.9 Bram Fischer 590.0 160.0 1190.0 49.2 0.0 274.7 –0.253 68.8 20.2 Francistown 482.3 46.2 1199.9 40.2 0.0 423.3 –0.342 66.2 13.6 Wonderboom 497.5 123.0 769.9 41.5 0.0 183.6 –0.095 49.9 18.5 405 Marc Muselli, Daniel Beysens Fig. 4. Mean rainfalls (mm) during the period 2001–2020. (a) Mean annual rainfall. (b) Mean monthly rainfall. (c) Maximum monthly rainfall. Red letters: Measurement sites (see Table 1); circles: biocrust sites according to Chen et al. (2020); right cross: Gobabeb site studied by Henschel et al. (2007) and Soderberg (2010); inclined cross: Potchefstroom site studied by Baier (1966). 3.4.1 Temporal correlation The temporal correlation between rainfall and dew yield is evaluated by a correlation coefficient r between the daily rain- fall, hr (t), and the time-shifted daily dew yield, hd (t+τ), esti- mated at the same location. The delay time τ corresponds to the previous and next days of time t and is counted in days in the interval [–31, +31]. The covariance between hd (t+τ) and hr (t) is calculated as: Ch t , h t+=ττ h t −h h t+ −h (6)  () ( ) () () ()() rd  r,, j r dj d  j =1 With σσ , the rain and dew standard deviation, respec- hh rd tively, one infers the correlation coefficient: Ch t , h t + τ ( ) ( )  rd rh ()t , h (t+= τ ) (7) rd  σσ hh rd Fig. 5. Difference between 2020 and 2011 of the annual rainfalls Considering that –1< r < 1, a negative correlation leads to an (mm). Red letters: Measurement sites (see Table 1); circles: opposite evolution of hr and hd, a positive correlation corre- biocrust sites from Chen et al. (2020); right cross: Gobabeb site studied by Henschel et al. (2007) and Soderberg (2010); inclined sponds to the two variables moving in the same trend and cross: Potchefstroom site studied by Baier (1966). r → 0 means that both variables are not correlated. 406 Mapping past, present and future dew and rain water resources for biocrust evolution in southern Africa The r correlation plots for each meteorological site accord- (iii) For τ > 0, some correlation can be observed for τ ≤ 3 ing to the three N scenarii are reported in Fig. 6. One observes days. For the Eros and Keetmanshop sites, r = 0.29 (N = 3) and the following: r = 0.18 (N = 1). For Mahikeng and Upington, r = 0.12 (N = 1) (i) For τ < 0, no correlations between dew and rain ampli- and r = 0.13 (N = 0). To a lesser extent, for Bram Fischer tudes are observed (mostly r < 0.05). It means that a rain event r = 0.097 for N = 1. These values thus indicate a weak but real at a given day does not explain dew events a few days earlier. positive correlation between rain and dew events. It means that, (ii) For τ = 0, all curves present negative values for r, with due to the increase of atmosphere humidity after rain events, dew events are more likely to be observed between one to three amplitude in the range between –0.3 and 0.1. This is due to the days after rainfalls. fact that, in the calculation of the dew yields in Section 2.1, one had to discard the days with rain. Fig. 6. Daily correlation coefficients rh (t ) , h (t + τ ) for time τ  −− 31 + 31 days. For stations with incomplete cloud cover data, the [ ] rd  curves are presented assuming N = 0 (blue), N = 1 (red) and N = 3 (grey). 407 Marc Muselli, Daniel Beysens The correlation dew-rain is most noticeable (Ondangwa, 400 12000 Eros, Keetmanshop; Upington, Mahikeng, Bram Fisher) when the distance from the ocean increases, the atmosphere RH then 10000 decreases (see Fig. 2d). In contrast, for stations close to the Rain C coast in arid climate (distance < 15 km) and with low annual Dew C 200 6000 rainfall (Hr < 50 mm) but large RH, such as Luderitz, Oran- Rain U jemund, Swakopmund and Walvis Bay, the correlation is very Dew U low regardless of the τ value. For the cities of Cape Town, Port Elizabeth and George, presenting a more temperate climate, the 2000 correlation shows at most a weak increase for τ < 4 to 5 days 0 0 (with r < 0.1). All these sites have an altitude below 200 m. Whatever is the N scenario, for altitudes between 800 m and 1700 m asl and > 200 km away from the ocean, the correlation Date is clearer with values of r showing a steady increase at Eros (1700 m asl, 266 km from the ocean), Keetmanshoop (1069 m 0.04 asl, 285 km from the ocean). Ondangwa (1099 m asl, 385 km from the ocean) and Bram Fischer (1349 m asl, 418 km from 0.035 the ocean) show a correlation with r > 0.1, respectively for τ = 0.03 2 and 3. For the other mountainous stations, the correlation Cape Town coefficients exhibit values that does not exceed 0.1, with τ = 5 0.025 for Gaborone (r = 0.0532) or τ = 3 for Maun (r = 0.0665). 0.02 3.4.2 Summed dew and rain yields 0.015 Upington 0.01 One now investigates the correlation between the cumulative 0.005 dew and rain monthly yields, sumhh = dt and () dd  0 0 04/2001 01/2004 10/2006 07/2009 04/2012 12/2014 09/2017 06/2020 Date sum()hh = dt , respectively, with t0 the starting time (see rr Table 1). Each data point will thus correspond to a monthly Fig. 7. Two typical evolutions (Upington U and Cape Town C mean value. For each month, a ratio at is calculated: sites) of dew and rain summed yields in the studied period (2001– ( ) 2020). The vertical dotted line corresponds to year 2010 where rainfalls begin to significantly decrease. (a) sum (hd) and sum(hr)  sum h ( )  with N = 0 missing data scenario (see text and Table 1). (b) Ratio at = (8) ()  sum h () a(t) = [sum(h )] / [sum(h )] . The horizontal straight lines are fits to d t r t  r a(t) = a0 = constant. In Fig. 7a the sum h , the sum ( h ) and their ratio a(t) ( ) d r Table 3. Ratio dew/rain summed amplitudes a (Eq. 9) according to for two sites (Upington and Cape Town sites) are reported (at different N assumptions for the missing data (see text and Table 1). small times the dispersion is large because the smoothing effect of the summation is still weak). In Cape Town, both rain and Site a (N = 0) a (N = 1) a (N = 3) 0 0 0 dew amounts are nearly linear during the research period, with Swakopmund 2.384 1.793 0.792 a decrease in rainfall rate after 2010 while the dew rate remains constant. In Upington, one observes a decrease in the rain Walvis Bay 2.444 1.841 0.832 amount and an increase in the dew amount after 2010. For sake Luderitz 1.154 0.940 0.569 of comparison in the whole time period, the data (Fig. 7b) can Ondangwa 0.023 0.016 0.006 be fitted to a mean constant value Oranjemund 0.858 0.651 0.282 a(t) = a (9) Eros 0.014 0.011 0.006 Keetmanshoop 0.020 0.014 0.006 The values of a according to the three N scenarios are Cape Town 0.028 0.028 0.028 summarized in Table 3. Taking into account all stations, the Upington 0.017 0.015 0.012 parameter a shows a large variability: a = 0.4 ± 0.8 (N = 0), Shakawe 0.011 0.011 0.011 a ± a ± = 0.3 0.6 (N = 1) and = 0.15 0.27 (N = 3). This 0 0 George 0.031 0.027 0.024 variability is due to the small number and erratic character of Maun 0.007 0.007 0.007 the precipitations in arid areas. When the very small quantities Mahikeng 0.013 0.011 0.007 of rain at these sites (Namib Desert: Oranjemund, Luderitz, Swakopmund and Walvis Bay) are removed, the variability of Port Elizabeth 0.026 0.026 0.026 values becomes much smaller ( a = 0.022 ± 0.008 (N = 0), 0 Gaborone 0.028 0.028 0.028 a = 0.020 ± 0.009 (N = 1) and a = 0.017 ± 0.011 (N = 3)). Bram Fischer 0.034 0.032 0.029 0 0 Francistown 0.018 0.018 0.018 The parameter a is mapped by the Kriging method in Fig. 8. Wonderboom 0.034 0.034 0.034 One can clearly observe the increasing importance of dew in a sum(h ) (mm) 01/2001 02/2002 03/2003 04/2004 05/2005 06/2006 07/2007 08/2008 09/2009 10/2010 11/2011 12/2012 01/2014 02/2015 03/2016 04/2017 05/2018 06/2019 07/2020 sum(h ) (mm) r Mapping past, present and future dew and rain water resources for biocrust evolution in southern Africa the total precipitations along the Namibian coast and more 3.5 Time period of events generally the dependence of a on longitude. It corroborates the fact that the distance from the ocean, which controls the atmos- Because the frequency or time period between rain events is phere RH (see Fig. 2), is the important parameter for the also an important parameter, which in itself can control the formation of dew. Toward the west, dew increases (Fig. 2) and biocrust growth, we investigate below this parameter for rain rain decreases (Fig. 4), leading to an increase in a. only, dew only and dew plus rain. For that purpose, one consid- The variation of the ratio a between 2020 and 2011 is ers the histogram of rain, dew and rain plus dew events (Fig. 10) reported in Fig. 9. One verifies the general increase of the where two important parameters can be extracted, the mean contribution of dew with respect to rain, especially towards time period between events, θ (in days) and the maximum time west. period, θM (in days). N = 0 N = 1 N = 3 Fig. 8. Map of ratio a0 corresponding to the average of a = sum(dew)/sum(rain) (Eqs. 8, 9) for the period 2001–2020 and three scenarios for missing N data (see text and Table 1). Letters: meteo sites; circles: biocrust sites according to Chen et al. (2020); right cross: Gobabeb site studied by Henschel et al. (2007) and Soderberg (2010); inclined cross: Potchefstroom site studied by Baier (1966). N = 0 N = 1 N = 3 Fig. 9. Variation between 2020 and 2011 of the ratio a0 = sum(dew)/sum(rain), corresponding to 3 scenarios for missing N data (see text and Table 1). Letters: meteo sites; circles: biocrust sites according to Chen et al. (2020); right cross: Gobabeb site studied by Henschel et al. (2007) and Soderberg (2010); inclined cross: Potchefstroom site studied by Baier (1966). Fig. 10. Typical histograms of time period θ (day) beetween (a) rain events, (b) dew events (c) rain and dew events. θ is the mean time and θ is the maximum time. Note that some dew or rain events can disappear in the histogram dew + rain because dew or rain events occur during the dew or rain time periods. 409 Marc Muselli, Daniel Beysens which can reach two orders of magnitudes. It results from the The evolution of θ and θ can be then considered (Fig. 0 M above observations that the dew events will determine the behav- SM2) and maps of mean values can be drawn for the consid- ior of the dew + rain time period (see Fig. SM2, Figs. 11–12). ered period (Fig. 11), with the difference between 2011 and When comparing the maps of dew and rain mean annual 2020 values (Fig. 12). Some curves are interrupted due to the times (Fig. 11) and dew and rain amplitudes (Figs. 2 and 4), lack of data. one observes a strong correlation between the zones of large One first notes from Figs. 10 and SM2 (in Supplementary Ma- times and low yield, and short times and high yield. This simp- terials) that the number of events is larger for dew than for rain. ly means that large water yields correspond to frequent dew or In addition, the timescale for mean and maximum time period rain events. between events is much larger for rain than for dew, a difference c d Fig. 11. Annual mean in the period 2001–2020 of the maximum time θ (day) (left column) and mean time θ (day) (right column). (a), (b): M 0 Rain; (c), (d): Dew; (e), (f): Rain+dew. Red letters: Measurement sites (see Table 1); circles: biocrust sites according to Chen et al. (2020); right cross: Gobabeb site studied by Henschel et al. (2007) and Soderberg (2010); inclined cross: Potchefstroom site studied by Baier (1966). 410 Mapping past, present and future dew and rain water resources for biocrust evolution in southern Africa Fig. 12. Difference between 2020 and 2011 of the maximum time θM (left column, day) and mean time θ0 (right column, day). (a), (b): Rain; (c), (d): Dew; (e), (f): Rain+dew. Red letters: Measurement sites (see Table 1); circles: biocrust sites from Chen et al. (2020); right cross: Gobabeb site studied by Henschel et al. (2007) and Soderberg (2010); inclined cross: Potchefstroom site studied by Baier (1966). The evolution of the mean and maximum time period between tively similar to the evolution of the rain and dew amplitudes 2001 and 2020 (Fig. SM2) show that mean and maximum time (Figs. 3 and 5). The inverse evolution of rain + dew times ra- periods evolve about the same way. The times keep nearly ther follows the dew evolution, as expected from the fact noted constant over the whole period for dew, noting some decrease above that the dew events mostly determine the behavior of the after 2010. Dew frequency is well correlated with the dew yield dew + rain times. amplitude, which remains constant or weakly increases in the same period (Fig. SM1 in Supplementary Materials). In contrast, 4 DISCUSSION AND RELATION WITH BIOCRUST for rain, while the times keep constant between 2001 and 2010, 4.1 Dew height dependence the times increase after 2010. This evolution corresponds well with the decrease of rain amplitude (Fig. SM1). Biocrust forms at the ground level while the calculation of The maps of evolution for the period 2011–2020 concerning Section 2.1 deals with a 30° tilted condenser at 1 m off the the differences in rain, dew and rain + dew times are reported in ground. Dew condensation can vary for three reasons. (i) RH Fig. 12. The evolution of mean and maximum times are qualita- can be height dependent. This is the case if wind speed is near 411 Marc Muselli, Daniel Beysens zero and soil is wet, for instance after a rain event. (ii) Air flow diminution of rainfall precipitations. On the Ghaap plateau in depends on height, and then, the heat and mass exchange with west center of South Africa, oscillations of rain precipitations the surrounding air. The variation of air flow velocity is known have been already noted by Tfwala et al. (2018) by analyzing to follow a log dependence above a roughness length z (see interannual rainfall variability on the Ghaap plateau. The cycles Section 2.3) where air flow velocity is zero. In addition to the last about 18–22 years in Postmarburg and between 12 and 16 forced air flow induced by wind, there exists a natural convec- years in Douglas. Another analysis of rainfall in South Africa tion induced by the substrate temperature colder than ambient by Zvarevashe at al. (2018) also concluded to quasi-decadal –1 air, with typical velocity 0.6 m s (Beysens et al., 2005; Clus et oscillations. The question whether the decrease we observed al., 2009). The log dependence of the windspeed and the pres- since 2010 is related to these oscillations or to the global ence of natural convection make the heat exchange coefficient climate change remains thus open. and then the mass diffusion coefficient, which determines the condensation yield, depend weakly of windspeed for values 4.4 Water availability and biocrust distribution –1 below ∼ 1 m s (measured at the standard height of 10 m). It As outlined in the Introduction, the amount of rain and dew results a weak dependence of condensation with height for such are considered as the main factors which influence the growth windspeeds, making the calculation of Section 2.1 valid at the of biocrust (see e.g. Kidron and Kronenfeld, 2020; Li et al., ground level. 2021a, b; Ouyang et al.; 2017; Pan et al., 2010; Zhuang and For larger windspeeds, the heat exchange coefficients will be Zhao, 2017). However, the frequency of rain events (longest larger, decreasing the dew yield. The latter will be then larger at period of drought) is the main factor according to Büdel et al. the ground level and the calculation of Section 2.1 will be a (2009). Although there are no studies concerning the effect of conservative value. frequency of dew events, one can reasonably assume that this 4.2 Comparison with direct dew yield measurements parameter also matters. Frequency of events and their amplitude are strongly corre- lated (see Section 3.5), the regions of large dew or rain ampli- The calculated dew yields can be compared with previous tudes corresponding to the regions of small dew or rain time works available in the literature. Baier (1966) reported dew and periods. Both criteria (amplitude, frequency) should thus corre- rainfall measurements from a weather station set at spond in the studied regions to the same characteristics favoring Potchefstroom (inclined cross in Fig. 2), located in the vast biocrust growth. interior plateau of South Africa (26°44’ S, 27°05’ E, 1352 m asl), The evolution between 2001 and 2020 is seen to exhibit two about 160 km from the Wonderboom site. During the period regimes, one from 2001 to 2010, where all parameters (dew and 1957–1958, the annual percentage of dew days was 45.7% (Won- rain amplitude, dew and rain frequency) keep nearly constant. derboom: 65.5%) with a mean annual dew amount of 12.6 mm The second regime, from 2010 to 2020, corresponds to a neat (Wonderboom: 19.9 mm). The values in Wonderboom are slight- decrease of rain amplitude and frequency of events, while dew ly larger, but the measurement time was earlier and we will see in the next Section that the general tendency is a positive dew amplitude and frequency either keeps constant or slightly in- yield evolution. crease. As far as rain is concerned, it should result in a decrease Dew collection were also carried out in 2006 by Henschel et of biocrust growth. However, dew yield is nearly constant or al. (2007) at Gobabeb (Namib Desert, 23°33.704 S, 15°02.466 E, increases after 2010. We are not aware of drastic changes in the distribution of biomass of biocrusts during the 2001–2020 right cross in Fig. 2) in Namibia's Central Namib Desert, situated period. This may be attributed to the increase of dew amplitude about 84 km from Walvis Bay and 110 km from Shakopmund. and frequency, which should act to compensate for the decrease The site elevation is 406 m. Only a few data were collected on a in rain precipitation. specially-designed 1 m passive dew collector. In July 2006, 3.3 mm of dew water was collected (12 dew days), 1.2 mm in Au- 5 CONCLUSION AND TRENDS FOR THE FUTURE gust (10 dew days), and 1.5 mm in September (10 dew days). Meteo data at Walvis Bay and Shakopmund are, however, avail- The determination of dew yield using a physical model and able only between 2010 and 2020. In these cities, the calculated rainfall data from 18 meteorological stations in Namibia, annual mean in July, August and September are nearly the same: 2.6 mm (July), 2.2 mm (August) and 2.2 mm (September) (N = Botswana and South Africa in the period 2001–2020 allow 0), 1.2 mm, 1.8 mm and 1.7 mm (N = 1) and 0.7 mm, 0.9 mm clear tendencies to be evaluated. Dew decreases from the East, and 0.9 mm (N = 3). Although not determined at the same dates, South, West coasts following the decrease in RH decrease, and these values compare relatively well with the above measured rainfalls diminish toward the West and North. A noticeable decrease in rain precipitations after 2010 and a corresponding values of 3.3 mm (July), 1.2 (August) and 1.5 mm (September). rise in dew yield are noted. It results in a steady increase of dew Between July 2008 and June 2009, Soderberg (2010) meas- contribution with respect to rain after 2010. In addition, a clear ured a greater amount of dew at Gobabeb, with 143 yearly dew increase in dew for three days in average after rainfall is events. The corresponding volume was 12.3 mm, which com- observed in the arid regions where the humidity is low. These pares relatively well with the Walvis Bay and Shakopmund results are corroborated with the frequency of dew and data for the same year: 21 mm (N = 0), 15.8 mm (N = 1), 7 mm rain events, which are closely correlated with dew and rain (N = 3). yields. The effect on biocrust is to show zones with less rain but 4.3 Variation in rain precipitation with increasing dew water. As far as rain is concerned, one As mentioned in Section 3.3, we observed a decrease of therefore should expect a decrease of biocrust growth. Howev- precipitation from west to east. All sites present a negative er, dew yield is nearly constant or even increases after 2010, variation in rain precipitation during 2001 to 2020. In which could possibly compensate the rain decrease as we are not aware of drastic changes in the distribution of biomass of particular, the decrease in precipitation is quite noticeable from biocrusts during the 2001–2020 period. 2010. In Namibia Lu et al. 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Control of insolation on 413 Marc Muselli, Daniel Beysens stalagmite growth, rainfall, and migration of the tropical rain Van de Beek, C.Z., Leijnse, H., Torfs, P.J.J.F., Uijlenhoet, R., belt in northern Namibia over the last 100 kyr, as suggested 2012. Seasonal semi-variance of Dutch rainfall at hourly to by a rare MIS 5b-5c stalagmite from Dante Cave. Palaeoge- daily scales. Adv. Water Resour., 45, 76–85. ogr., Palaeoclimatol., Palaeoecol., 535, 109348. Weather Underground database, 2021. https://www.wunder Soderberg, K.S., 2010. The role of fog in the ecohydrology and ground.com biogeochemistry of the Namib Desert. MSc. Thesis, Univer- Yao, X., Xia, B., Kidron, G.J., Hu, K., 2019. Respiration rate of sity of Cape Town, Department of Environmental Sciences, moss-dominated biocrust and their relationships with tem- University of Virginia. perature and moisture in a semiarid ecosystem. Catena, 183, Tomaszkiewicz, M., Najm, A., Beysens, D., Alameddine, I., 104195. 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Received 20 June 2021 Accepted 1 October 2021 414 Mapping past, present and future dew and rain water resources for biocrust evolution in southern Africa –1 Appendix 1 – Dew yield calculation the wind-speed (V, m s ) at 10 meters of the ground, recorded every Δt = 1h., we compute an hourly yield h (mm) corre- We give below in Table SM1 an example of determination sponding to evaporation (h < 0) or condensation (h > 0) events. i i of dew yield from Section 2.1. The model (Eq. 2) is applied to By discarding evaporation (hi < 0) and rain events, the cumula- one night (March 21–22, 2010) in Cape Town (South Africa). tive dew yield h for each night is computed. For the studied Considering the sky cloud cover (N, oktas), the air (Ta, °C) and night, h = 0.185 mm. dew (Td, °C) temperatures, the relative humidity (RH, %) and Table SM1. Exemple of calculation of dew yields from meteorological data. Date Hour N V T RH T T –T h h > 0 sum(h ) a d d a i i i (dd/mm/aaaa) (hh:mm) (oktas) (m/s) (°C) (%) (°C) (°C) (mm) (mm) (mm) 21/03/2010 12:00 5 6.1 22 69 16 –6 –0.030 0.000 0.000 21/03/2010 13:00 5 7.2 23 65 16 –7 –0.035 0.000 0.000 21/03/2010 14:00 3 7.8 22 69 16 –6 –0.030 0.000 0.000 21/03/2010 15:00 1 7.8 22 69 16 –6 –0.030 0.000 0.000 21/03/2010 16:00 1 6.1 22 69 16 –6 –0.030 0.000 0.000 21/03/2010 17:00 1 5.6 21 68 15 –6 –0.030 0.000 0.000 21/03/2010 18:00 1 4.7 19 83 16 –3 –0.015 0.000 0.000 21/03/2010 19:00 0 3.1 18 88 16 –2 0.014 0.014 0.014 21/03/2010 20:00 0 0.6 18 88 16 –2 0.014 0.014 0.027 21/03/2010 21:00 0 1.9 15 94 14 –1 0.019 0.019 0.046 21/03/2010 22:00 0 3.1 14 100 14 0 0.024 0.024 0.070 21/03/2010 23:00 0 3.1 17 88 15 –2 0.014 0.014 0.084 22/03/2010 00:00 0 3.1 17 88 15 –2 0.014 0.014 0.098 22/03/2010 01:00 0 3.1 17 94 16 –1 0.019 0.019 0.117 22/03/2010 02:00 0 4.2 17 94 16 –1 0.012 0.012 0.128 22/03/2010 03:00 0 5.3 17 100 17 0 0.000 0.000 0.128 22/03/2010 04:00 0 3.6 18 94 17 –1 0.018 0.018 0.146 22/03/2010 05:00 0 3.1 17 100 17 0 0.023 0.023 0.170 22/03/2010 06:00 1 3.6 17 94 16 –1 0.015 0.015 0.185 22/03/2010 07:00 1 4.7 18 88 16 –2 –0.010 0.000 0.185 22/03/2010 08:00 1 6.7 21 83 18 –3 –0.015 0.000 0.185 22/03/2010 09:00 1 7.8 24 69 18 –6 –0.030 0.000 0.185 22/03/2010 10:00 1 9.2 25 61 17 –8 –0.040 0.000 0.185 22/03/2010 11:00 1 9.2 26 57 17 –9 –0.045 0.000 0.185 22/03/2010 12:00 1 10.8 25 65 18 –7 –0.035 0.000 0.185 th Appendix 2 – Kriging method the i location, s the predicted location and p the number of measured data. Kriging is a stochastic spatial interpolation method that pre- With the Kriging method, the λ weighted coefficients are dicts the value of a natural phenomenon at non-sampled sites by not only based on the distance between the surveyed points and an unbiased, minimal variance linear combination of observa- the forecast location, but also on the general spatial organiza- tions of the phenomenon at nearby sites. The Kriging tool as- tion of the surveyed points. To use the spatial arrangement in sumes that the distance or direction between the sample points the weighing, the spatial autocorrelation is quantified. Thus, in reflects a spatial correlation that can explain the surface varia- ordinary Kriging, the weighting λ depends on the distance tions. The Kriging tool applies a mathematical function to all i points, or certain determined points, located within a specific from the forecast location and the spatial relationships between radius. It determines the output value of each location. the values recorded around it. The Kriging tool is particularly suitable for cases where it is The experimental semi-variogram can be estimated from known that there is a spatial correlation of distance or a direc- point pairs: tional deviation in the data. Kriging deduces, by weighting nh ( ) existing readings, the probable values of unmeasured locations. γˆhZ=−sZs+h ² () () ( )  ii  2nh () i =1 To calculate the interpolated data Zs() at a specific location s0, the general formula of ordinary Kriging (OK) method con- where nh=− Card s,/ s s s≈ h () {( ) } ij i j sists of a weighted sum of the data (Goovaerts, 1997): with “card” represents the number of elements for the given ˆ condition. Zs() = λ Zs( ) 0 ii Classically, estimated semi-variogram are fitted by a spheri- i =1 cal variogram model as proposed in previous studies on rainfall th Here Zs ( ) corresponds to the measured value at the i lo- spatial estimation (Bargaoui and Chebbi, 2009; Lepioufle et al., cation, λ the ponderation coefficient to determine and relate to 2012; Rahmawati, 2020; Van de Beek et al., 2012). 415 Marc Muselli, Daniel Beysens Supplementary Materials time θ (day) and the maximum time θ (day) between (a) rain 0 M (orange line), dew (blue short interrupted line) and rain plus We present below supplementary materials for additional dew events (green long interrupted line). calculated data. Table SM2 gives the correlation between the sky conditions Figure SM1 reports the evolution of the dew summed values and the cloud cover in oktas according to NOAA. sum(h ) (dew, mm, full blue line) and the rain summed values d Table SM3 reports the yearly (Hd) and monthly (hd) mean, sum(hr) (rain, mm, interrupted red line) for the studied sites. minimum and maximum dew yields calculated from meteoro- Figure SM2 is concerned with the evolution of the mean logical data. Fig. SM1. Evolution of the summed values sum(h ) (dew, mm, full blue line) and sum(h ) (rain, mm, interrupted red line) for the studied d r sites. The vertical interrupted line corresponds to a significant decrease of rainfall after 2010 with dew yield remaining constant or weakly increasing. 416 Mapping past, present and future dew and rain water resources for biocrust evolution in southern Africa 417 Marc Muselli, Daniel Beysens 418 Mapping past, present and future dew and rain water resources for biocrust evolution in southern Africa Fig. SM2. Evolution of mean time θ (day) and maximum time θ (day) between (a) rain (orange line), dew (blue short interrupted line) 0 M and rain plus dew events (green long interrupted line). Some curves are interrupted because data are missing. 419 Marc Muselli, Daniel Beysens Table SM2. Correlation between sky conditions and cloud cover according to NOAA’s national weather service glossary, 2021. The abbreviations for sky conditions are the following: CLR = Clear; FEW = few; SCT = Scattered; BKN = Broken; OVC = Overcast. Observation N (oktas) CLR 0 FEW 1 SCT 3 BKN 5 OVC 8 Table SM3. Yearly (Hd) and monthly (hd) mean, minimum and maximum dew yields calculated from meteorological data. The mean evo- lution data during from 2001 to 2020 are fitted to Eq. (5) with free parameters α = dh / dt and hd,0. Red values correspond to a decrease dd of dew yield evolution, blue values to an increase. Cloud coverage N is assumed to be 0, 1 or 3 oktas when cloud cover data are missing (see text and Table 1). year Hd (mm) hd (mm) N α hd,0 Site frequency –1 (oktas) (mm month ) (mm) Mean Min Max Mean Min Max (%) 0 37.7 31.2 45.5 3.1 0.0 6.8 –0.002 3.2 85.6 Swakopmund 1 28.4 22.9 34.6 2.4 0.0 5.4 –0.001 2.4 84.9 3 12.6 9.4 15.9 1.0 0.0 2.8 –0.001 1.1 79.1 0 38.2 31.7 46.1 3.2 0.0 6.9 –0.002 3.2 85.8 Walvis Bay 1 28.8 23.3 35.1 2.4 0.0 5.4 –0.001 2.4 85.0 3 12.8 9.6 16.1 1.0 0.0 2.9 –0.001 1.1 79.3 0 16.2 3.6 26.3 1.3 0.0 4.9 0.001 1.3 42.3 Luderitz 1 12.6 2.8 21.4 1.0 0.0 4.3 0.001 0.1 40.3 3 6.6 1.3 13.3 0.6 0.0 3.0 0.000 0.5 34.8 0 4.9 0.4 13.5 0.4 0.0 3.7 –0.004 0.6 25.3 Ondangwa 1 3.5 0.3 9.8 0.3 0.0 2.8 –0.003 0.5 22.0 3 1.4 0.1 3.8 0.1 0.0 1.2 –0.001 0.2 13.5 0 42.5 32.4 56.8 3.5 0.9 8.2 0.003 3.2 81.5 Oranjemund 1 32.8 23.9 45.2 2.7 0.5 6.8 0.003 2.4 80.4 3 15.4 9.6 24.3 1.3 0.2 4.1 0.003 1.0 70.6 0 4.6 1.4 8.9 0.4 0.0 2.6 –0.004 0.6 16.7 Eros 1 3.5 0.9 7.0 0.3 0.0 2.1 –0.003 0.5 14.6 3 1.9 0.3 3.8 0.2 0.0 1.1 –0.002 0.3 13.3 0 3.0 0.8 5.7 0.3 0.0 1.8 –0.003 0.5 18.4 Keetmanshoop 1 2.2 0.5 4.2 0.2 0.0 1.4 –0.002 0.3 15.3 3 0.9 0.2 2.0 0.1 0.0 0.8 –0.001 0.1 8.7 Cape Town – 18.3 8.9 24.1 1.5 0.0 5.1 0.000 1.6 58.2 0 5.5 0.4 13.8 0.5 0.0 2.9 0.000 0.5 27.0 Upington 1 5.1 0.4 13.2 0.4 0.0 2.8 0.000 0.4 26.6 3 4.5 0.4 12.4 0.4 0.0 2.6 0.001 0.3 25.7 Shakawe – 8.0 3.5 16.5 0.7 0.0 4.5 0.003 0.4 43.9 0 27.0 12.8 38.5 2.2 0.0 4.7 0.004 2.1 64.5 George 1 25.7 12.8 37.4 2.1 0.0 4.7 0.003 1.9 64.3 3 23.3 12.8 35.3 1.9 0.0 4.7 0.002 1.6 64.0 Maun – 6.9 1.8 18.0 0.6 0.0 4.9 0.003 0.3 40.3 0 9.8 0.1 21.7 0.8 0.0 4.7 0.003 0.6 37.6 Mahikeng 1 8.1 0.1 18.1 0.7 0.0 4.1 0.002 0.5 35.8 3 5.5 0.1 12.2 0.5 0.0 2.9 0.001 0.3 33.2 Port Elizabeth – 20.0 14.3 26.8 1.7 0.0 4.5 0.000 1.6 64.1 Gaborone – 16.2 6.6 26.0 1.4 0.0 5.9 –0.001 1.4 57.8 0 26.5 14.4 38.8 2.2 0.0 7.7 0.001 2.2 66.4 Bram Fischer 1 24.0 11.9 38.7 2.0 0.0 6.8 0.000 2.2 65.6 3 20.1 8.7 38.4 1.7 0.0 5.6 0.000 2.2 64.8 Francistown – 12.1 4.9 23.8 1.0 0.0 4.2 –0.004 1.4 58.3 Wonderboom – 19.9 8.0 27.4 1.7 0.0 5.0 0.000 1.7 65.5 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Hydrology and Hydromechanics de Gruyter

Mapping past, present and future dew and rain water resources for biocrust evolution in southern Africa

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J. Hydrol. Hydromech., 69, 2021, 4, 400–420 ©2021. This is an open access article distributed DOI: 10.2478/johh-2021-0030 under the Creative Commons Attribution ISSN 1338-4333 NonCommercial-NoDerivatives 4.0 License Mapping past, present and future dew and rain water resources for biocrust evolution in southern Africa 1, 2 2, 3* Marc Muselli , Daniel Beysens Università di Corsica Pasquale Paoli, Avenue du 9 septembre, BP 52, 20250 Corte, France. OPUR, 2 rue Verderet, 75016 Paris, France. Physique et Mécanique des Milieux Hétérogènes, CNRS, ESPCI Paris - PSL University, Sorbonne Université, Sorbonne Paris Cité, 10 rue Vauquelin, 75005 Paris, France. Corresponding author. Tel.: +33(0)689864717. E-mail: daniel.beysens@espci.fr Abstract: Biocrust sustainability relies on dew and rain availability. A study of dew and rain resources in amplitude and frequency and their evolution is presented from year 2001 to 2020 in southern Africa (Namibia, Botswana, South Africa) where many biocrust sites have been identified. The evaluation of dew is made from a classical energy balance model using meteorological data collected in 18 stations, where are also collected rain data. One observes a strong correlation between the frequency of dew and rain and the corresponding amplitudes. There is a general tendency to see a decrease in dew yield and dew frequency with increasing distance from the oceans, located west, east and south, due to decreasing RH, with a relative minimum in the desert of Kalahari (Namibia). Rain amplitude and frequency decreases when going to west and north. Short-term dew/rain correlation shows that largest dew yields clearly occur during about three days after rainfall, particularly in the sites where humidity is less. The evolution in the period corresponds to a decrease of rain precipitations and frequency, chiefly after 2010, an effect which has been cyclic since now. The effect is more noticeable towards north. An increase of dew yield and frequency is observed, mainly in north and south-east. It results in an increase of the dew contribution with respect to rain, especially after 2010. As no drastic changes in the distribution of biomass of biocrusts have been reported in this period, it is likely that dew should compensate for the decrease in rain precipitation. Since the growth of biocrust is related to dew and rain amplitude and frequency, future evolution should be characterized by either the rain cycle or, due to global change, an acceleration of the present tendency, with more dew and less rainfalls. Keywords: Biocrust; Dew and rain evolution; Dew/rain ratio; Dew/rain correlation; Southern Africa; Climate change. 1 INTRODUCTION enhanced effect between dew and artificially revegetation ecosystems in the arid desert ecosystem in Shapotou (China). Li Biocrust are typically found in drylands with arid or semi- et al. (2021a, b), in recent papers, determine that biocrust arid ecosystems. In great interaction with the soil, biocrust benefits from non-rainfall water deposition and modify their concern cyanobacteria, lichens, algae and mosses. These organ- distribution in drylands soils. Dewfall can be presented as a isms contribute strongly in the ecosystem’s functioning and critical source of water in deserts environments allowing to plant organization and are present all around the world. determine the sustainability of sand to stabilize planted Numerous works detail their physical, chemical and biologi- vegetation (Zhuang and Zhao, 2017). Dew, fog and rain can cal characteristics in semi-arid or arid climates. Negev (Jacobs play an important role for the development of biocrust in semi- et al., 2002; Kidron and Tal, 2012), Europe (Raggio et al., arid regions. Kidron (2019) suspects dew to be a necessary 2021), Spain (Cano-Díaz et al., 2018), China (Yao et al., 2019), water source for cyanobacteria. Biocrust alter non-rainfall USA (Aguirre-Gutiérrez et al., 2019) are a few examples. distribution by depth, concentrating it in the surface (Li et al., According to Chen et al. (2020), biocrust correspond to 30% of 2021a, b). Biocrust can boost the use of non-rainfall water global drylands. It is in China, Australia, North America and according to Ouyang et al. (2017). Büdel et al. (2009) conclude Spain in Europe that are found the more studied biocrust sites. their study by noting that the time frequency of rain In the present study, a representative area for biocrust studies precipitations is more important than their amount. was chosen in a less investigated area, the southern part of The amount and frequency of rain and dew are then the main Africa. Namibia, South Africa and Bostwana are the main factors which influence the growth of biocrust. This paper aims countries involved in this study, representing 18 sites of meas- to evaluate the evolution of these contributions to over a long urement (7 in Namibia, 7 in South Africa and 4 in Bostwana, period of time (20 years, from 2001 to 2020) in order to put in respectively). One should note that these locations are based on evidence the long term trend and extrapolate to the near future. previous works of a few scholars within certain research sites Because certain data are lacking before 2011, a few analyses and cannot obviously replace an objective map. A map of soil are restricted to 10 years (2011–2020). can help to locate biocrust, it is given in Fig. 1 together with the The paper is organized as follows. After having reported on above studied sites. measurements and methods in Section 2, mainly concerning the Moisture from atmosphere (rainfall, fog, dew, vapor physical model used to determine the dew yields, Section 3 absorption) plays an important role in sustaining life in arid or is devoted to the main results with maps i) for dew and rain at- semi-arid climates. Pan et al. (2010) concluded on the mutual mospheric deposition, ii) cumulative rainfall and dew yields 400 Mapping past, present and future dew and rain water resources for biocrust evolution in southern Africa comparisons and iii) short time and longtime evolution of dew Namibia (824 292 km² surface area). The country shows and rainfalls yield and frequency. A Section 4 is devoted to dis- three different climates, the most prevalent being semi-arid cussions and relation of the rain and dew studies with biocrust. (Köppen-Geiger classification BSh) and hot desert (BWh). The less frequent is cold desert climates (BWk). The climate is characterized by great differences in day and nighttime temper- 2 METEOROLOGICAL DATA AND METHODS atures, low rainfall and overall low humidity. Along the coast, 2.1 Dew yield estimation from meteorological data the average annual precipitation does not exceed 15 mm. Inside the country, the continental plateau has a more contrasted situa- In order to estimate the dew potential, Beysens (2016) tion with abundant precipitations (> 500 mm). The dry season, developed an energy balance model which, thanks to some between May to October, correspond to little or no rainfall approximation, uses only a few classical meteorological data during July and August. Wildlife uses mainly waterholes and without adjustable parameters: cloud cover (N, oktas), wind −1 rivers when the water sources dry up. In desert areas, the aver- speed (V, m s ), air temperature (T , °C), air relative humidity age minimum temperature is cold and can fall below freezing at (RH, %) and dew point temperature (T , °C). Near the ground night. The wet season, between November to April, present level where dew forms, in the atmospheric boundary layer, the daytime temperatures of about 30 °C with the first rains ob- contribution from water vapor (about 0.2–2% by volume) and, served in November (mean rainfall 26 mm to a maximum in to a lower extent, carbon dioxide (about 0.03% in volume) is of January with 91 mm). Sometimes, torrential downpours are great importance for the radiative balance, with radiation from observed in the afternoon up to March and April, where rainfall water vapor being by far the more important of the two. The –1 decrease and stops before the dry season. results are concerned with dew yields h [mm (Δt) ] where Δt Botswana (581 730 km² surface area). The climate is charac- corresponds to the period (in hours) of the analyzed data. It is terized as hot semi-arid, the dominant climate (Köppen-Geiger assumed that the substrate emissivity is unity (which is close to classification BSh), and hot desert (BWh). During summer the emissivity ≈ 0.98 of a wet substrate, see Trosseille et al., months (November–March), a rainy season is observed with 2021) and is thermally insulated from below. The data can be high temperatures. The mean annual rainfall varies from over obtained from the airport meteo stations by using the following 650 mm in the extreme northeast area (Chobe District) to a formulation: minimum of 250 mm in the extreme southwest part (Kgalagadi District). The winter season during May to August corresponds Δt  hH=+ LRE (1) ()  to the dry season with less than 10% of the annual rainfall. The  variability of rainfall increases while the quantity decreases toward the south and west. The factor Δt is the measurement period of the data (here 6, South Africa (1.22 million km² surface area). The country 3 or 1 h. depending on the stations). The data for h > 0 corre- corresponds to a subtropical area, influenced by the vicinity of spond to condensation and h < 0 to evaporation, which have to the oceans along the coastlines and the altitude of interior be discarded. The quantity HL represents the convective heat plateau (1 500 m in the dolerite-capped Roggeveld scarp in the losses between air and condenser, with a cut-off for windspeed south-west, to a height of 3 482 m in the KwaZulu-Natal Dra- −1 V > V0 = 4.4 m s where condensation vanishes: kensberg). The country has several climatic zones depending on its geography: in the northwest, near the Atlantic coast stretch-  Δt  ing to the center of the country, the climate is mainly character-  0.06 TT−+RE ifV <V ()  da 0  h = 12 (2)  ized by arid lime (BWh) or cold (BWk) deserts. In the south-east, the country offers a temperate climate with dry and 0 if V >V  0 hot (Csa) or warm (Csb) summers. Finally, along the southern coast of the country, one finds a hot (BSh) or cold (BSk) arid The quantity RE is the available radiative energy, which de- climate with steppes but also a temperate zone, along the ocean pends on air water content (measured by the dew point tem- between the towns of George and Port Elisabeth with dry perature Td, in °C), site elevation H (in km) and cloud cover N winters and hot summers (Cwa). The eastern part of the coun- (in oktas): try, which is more mountainous, is characterized by a predomi- nantly temperate climate, without a dry season, with hot to  1+− 0.204323HH 0.0238893 −  RE=× 0.37 temperate (Cfb) or cold (Cfc) summers. Mean rainfall is about 23 −  18.0132 −+ 1.04963HH 0.21891 ×10T () d 460 mm with a large dispersion according to the location.  Usually, the western Cape presents major rainfalls in winter T + 273.15 N  d whereas the rest of the country exhibits summer rainfalls. ×− 1   285 8 The spatial distribution of rainfall between Namibia,   Bostwana and South Africa presents some differences in space (3) and time (New et al., 2000). In Namibia, for the locations of By filtering the rain and fog events and integrating the time Dante Cave at the north of the country, summer rainfall is ob- series on a daily time-step corresponding to h > 0, calculated served from October to April, with mean annual rainfall be- daily yields and their cumulated values are obtained. We give –1 tween 500 and 600 mm yr , a value much less than the poten- –1 an example of calculation in Appendix 1. tial evapotranspiration estimated to 2900 mm yr (Railsback et al., 2019). A similar behavior is observed at the frontier be- 2.2 Studied area tween Bostwana and South Africa (27°S, 21°E), with summer rainfall. The situation is more complex in South Africa. Ac- The study area (Fig. 1) is characterized by a spatial extent of cording to the location, one observes winter rainfall as in Cape about 3 000 000 km between 15° to 35° south latitude and 13° Town with precipitations mainly during April to September, weak precipitations but year-round in George and summer to 30° for east longitude. In the following are detailed the dif- rainfall with a dry winter in Pretoria (Railsback et al., 2019). ferent climate characteristics of the countries. 401 Marc Muselli, Daniel Beysens Fig. 1. Map of soils in the studied area (from Jones et al., 2013). Black rectangle and black letters are airport stations. The interrupted blue rectangle corresponds to the biocrust sites (green circles, see Chen et al., 2020). Table 1. Sites where atmospheric data are collected (7 stations in Namibia, 4 stations in Bostwana and 7 stations in South Africa). They are sorted according to their longitude (west to east). The sky condition data availability (% of the total sky conditions data) is reported for each station. Country Site Abbreviations Latitude Longitude Altitude Distance to data Sky conditions Name (m asl) the sea (km) period data (%) Namibia Swakopmund SM 22° 40' 0'' S 14° 34' 0'' E 61 8 2010-2020 52.4 Namibia Walvis Bay WB 22° 58′ 47″ S 14° 38′ 43″ E 86 14 2010-2020 52.4 Namibia Luderitz L 26° 41′ 15″ S 15° 14′ 34″ E 131 1 2006-2020 0.0 Namibia Ondangwa OD 17° 52′ 41″ S 15° 57′ 09″ E 1099 385 2011-2020 47.7 Namibia Oranjemund OJ 28° 35′ 05″ S 16° 26′ 48″ E 5 6 2005-2020 0.0 Namibia Eros E 22° 36′ 44″ S 17° 04′ 50″ E 1699 266 2011-2020 45.2 Namibia Keetmanshoop K 26° 32' 13'' S 18° 06′ 40″ E 1069 285 2011-2020 40.0 South Africa Cape Town C 33° 58′ 10″ S 18° 35′ 50″ E 46 3 2001-2020 100.0 South Africa Upington U 28° 24′ 04″ S 21° 15′ 35″ E 844 432 2001-2020 77.3 Botswana Shakawe SK 18° 22′ 25″ S 21°50′ 00″ E 1008 895 2005-2020 100.0 South Africa George G 34° 0' 20'' S 22° 22' 42'' E 197 7 2001-2020 89.9 Botswana Maun MN 19° 59' 0'' S 23° 26' 0'' E 945 1106 2001-2020 100.0 South Africa Mahikeng MK 25° 48' 27"S 25° 32' 40" E 1274 680 2001-2020 65.6 South Africa Port Elizabeth P 33° 59' 5'' S 25° 37' 2'' E 68 3 2001-2020 100.0 Botswana Gaborone GB 24° 33′ 19″ S 25° 55′ 06″ E 1006 695 2001-2020 99.9 South Africa Bram Fischer B 29° 05′ 38″ S 26° 18′ 14″ E 1349 418 2001-2020 76.1 Botswana Francistown F 21° 10' 0'' S 27° 29' 0'' E 1002 726 2002-2020 100.0 South Africa Wonderboom W 25° 39′ 13″ S 28° 13′ 27″ E 1240 460 2005-2020 88.6 2.3 Extraction data 0.1 m in flat areas) where V = 0. Available data were extracted from the online data base “Weather Underground” (Weather All ground stations are installed on international or national Underground database, 2021) during a period of maximum 20 airports where standard meteorological parameters are meas- years (2001–2020) with a minimum of 10 years (2011–2020) ured. The meteorological stations meet the data measurement depending on data availability (Table 1). standards of the World Meteorological Organization. Air T Dew yields have been computed from Eq. (2) using the (°C) and dew T (°C) temperatures, relative humidity (RH, %), above standard meteorological databases extracting air and dew atmospheric pressure (P, Pa) are measured in a meteorological point temperatures (T and T , °C), relative humidity (RH, %), a d –1 –1 −1 shelter, 1.5 m from the ground. The windspeed (V, km h ) and wind speed (km h to be transformed in m s ), wind direction direction (sectors or degrees) are measured at 10 m from the (sectors), absolute pressure (hPa) and sky cover. An hourly ground. Note that wind speed can be extrapolated at any height time-step for measured data is accessible except for Oran- z above the ground by the classical logarithmic variation (see jemund and Luderitz (Namibia) where two time-steps are avail- able (Oranjemund: 6 h on 2005–2014 and 3 h on 2014–2020);    z 10 Vz =V ln / ln e.g. Pal Arya, 1988) () where V10 is    Luderitz (6 h on 2006–2012 and 3 h on 2012–2020). zz cc  Wind direction values in degrees have been computed from windspeed at 10 m and z is the roughness length (generally ≈ wind direction sectors (N, NNE, NE, E, ESE, SE, S, etc.) using 402 Mapping past, present and future dew and rain water resources for biocrust evolution in southern Africa a standard law of proportionality: 0° for north, 180° for south itz, Swakopmund and Oranjemund) benefit from high dew –1 and calculation of all intermediate values with respect to these yields (> 10 mm yr ) mainly explained by the high humidity references. due to the vicinity of the Atlantic Ocean. For example, mean –1 The sky cover was considered variable if it varies by one or dew yields in the range 12.6 to 38.2 mm yr (for N = 0, 1, missing more of the reported values (CLR, FEW, SCT, BKN, or OVC) 3) have been obtained in Swakopmund and Walvis Bay, located during the period of observation (NOAA’s national weather near the Namib national Park, corresponding to mean monthly service glossary, 2021). Cloud cover in oktas was computed dew yields between 2.8 and 6.9 mm. For both stations, dewy from the nightly observation of sky cover using the correspond- days represent between 79.1 (Swakopmund, N = 3) and 85.8% ence listed in Table SM2 in Supplementary Materials, which (Walvis Bay, N = 0) of the year. On the other hand, the stations was used in a previous work (Muselli et al., 2020). However, established in the interior of the country suffer from very low –1 cloud cover is sometimes not available at night on some sites annual dew yield (< 5 mm yr ). For example, Eros, Keetmans- (the missing percentage of total values is noted for each site in hoop and Ondangwa, respectively located at about 250 and Table 1). When the sky conditions data are unavailable, we 350 km from the ocean, exhibit annual dew yields less than imposed to these sites three possible values, corresponding to 4.9 mm. In Keetmanshoop, monthly dew yields are very weak the most probable: N = 0, 1 and 3. with a mean of 0.1–0.3 mm and a monthly maximum of up to Measured rainfall data, available on a daily time step, are 1.8 mm. For Eros and Keetmanshoop, only 10–20% of the days extracted from the meteorological data base (Infoclimat data- are dewy (min = 8.7% and max = 18.4%), while for Ondangwa base, 2021). All data are obtained for the same stations as used it is 25% or even 15% (N = 0 for missing data) or even one for dew calculation except for Swakopmund where the rainfall day a week in the most unfavorable case (N = 3 for missing data of Walvis Bay are used (both sites are only 25 km apart). data). The situation is more homogeneous in Botswana. The mean 2.4 Kriging maps annual dew yields are between 6.9 and 16.2 mm depending on the sites (annual dew yield min = 1.8–6.6 mm and max = 16.5– Kriging methodologies are mainly used for mapping spatial 26 mm), with monthly yields averaging between 0.6 and 1.4 distribution of a given variable. The classical algorithm is pre- mm (min = 0 mm and max = 4.2–5.9 mm). sented in Appendix 2. Belkiri et al. (2020) use Kriging to study Except in Upington (mean < 5.5 mm), located in the north- ground water composition. Tomaszkiewicz et al. (2016) pro- ern Cape Province of South Africa on the banks of the Orange pose ordinary Kriging to develop dew maps integrating project- River, and Mahikeng, near to the Bostwana frontier (mean < ed climate changes in the Mediterranean basin. Martinez et al. 9.8 mm), all the South Africa country exhibits mean annual dew (2017) present median polish Kriging (MPK) for space-time yields more than 15 mm. For example, Cape Town, Port Eliza- analysis of monthly precipitation in Colombia. Pue et al. (2021) beth and George cities, on the south coast, or Wonderboom and introduce a Kriging-based Gaussian process for the evaluation Bram Fischer (near respectively Pretoria and Johannesburg), for the prediction of soil water retention in tropical and temper- present averaged annual dew yields of more than 18.3 mm, and ate climates. Other studies combine Kriging models for the up to 27 mm. Whereas the maximum monthly dew yields do not estimation of rainfall with Lagrangian (Amani and Lebel, 1997) exceed 4.7 mm in Upington and Mahikeng, the other cities pre- or Bayesian (Lima et al., 2021) approaches. sent monthly dew yields larger than 4.5 mm, and up to 7.7 mm. The spatial distribution of dew yields was determined by Kriging (Fig. 2, for N = 0, 1, 3 for missing data). Maps of mean 3 RESULTS annual dew yields are presented in (Figs. 2a, b, c). As expected 3.1 Evolution and described in the literature (Henschel et al., 2007; Soder- berg, 2010), dew exhibits the highest yields along the west For each site, dew (subscript i = d) and rain (subscript i = r) coast of Namibia corresponding to the Namib Desert. This monthly yields hi (mean, min, max in mm) are computed. desert represents about 81 000 km² and stretches over 1,500 km Annual dew yield (mm) is deduced by adding the monthly hi: along an 80 to 160 km wide north-south coastal strip along the Atlantic Ocean. One also clearly observes the decrease in yields Hh = ()t (4) ii  inland, especially from the central plateau towards the desert of t =1 Kalahari representing a surface of 900 000 km² with 600 000 km² in Namibia. However, one notes that in these critical areas, In order to estimate the evolution, monthly dew yields can monthly dew yields can reach mean and maximal values up to be fitted by a linear regression on the measured period: 2–3 mm and 6–8 mm, respectively. Note that the biocrust sites are located in regions of moderate dew yield. ht =+ α t h (5) ( ) ii i,0 More generally, there is a tendency to see a decrease in dew yield with increasing distance from the oceans, located W, E With t in month, the coefficient α = dh / dt represents the ii and S. A clear decrease in nocturnal RH from west to east is monthly evolution rate. obvious (Fig. 2d), with the largest dew yields (Fig. 2a, b, c) corresponding to the regions of highest RH. 3.2 Dew yields 3.2.2 Evolution map 2001–2020 3.2.1 Data description In Fig. SM1 (Supplementary Materials) are plotted the evo- Mean, minimum and maximum dew yields are calculated on monthly and yearly time bases and reported in Table SM3 in lution of the summed value of dew yield, sum()hh = dt Supplementary Materials. The calculated annual dew yields dd  show significant variations depending on the sites studied even 0 within the same country (Fig. 2 and Table SM3). on a monthly basis, with t the starting year (see Table 1). The In Namibia, the sites on the west coast (Walvis Bay, Luder- dew rate is either nearly constant during the period 403 Marc Muselli, Daniel Beysens Fig. 2. (a, b, c): Map of annual dew yield Hd (in mm) in the period 2001–2020 corresponding to three scenarios for missing N data (see text and Table 1). (d): Mean nocturnal RH (%) during dew events. Red letters: Meteo sites (see Table 1); circles: Biocrust sites according to Chen et al. (2020); right cross: Gobabeb site studied by Henschel et al. (2007) and Soderberg (2010); inclined cross: Potchefstroom site studied by Baier (1966). N = 0 N = 1 N = 3 Fig. 3. Difference between 2020 and 2011 annual dew yields (mm) for three scenarios corresponding to the missing N data (see text and Table 1). Red letters: Measurement sites (see Table 1); circles: biocrust sites according to Chen et al. (2020); right cross: Gobabeb site studied by Henschel et al. (2007) and Soderberg (2010); inclined cross: Potchefstroom site studied by Baier (1966). (Swakopmund, Walvis Bay, Eros, Keetmanshoop, Cape Town, By considering the period where meteorological data are Port Elizabeth, Gaborone, Bram Fischer) or increases (Luderitz, available on all sites (2011–2020), one can determine the evolu- Oranjemund, Upington, Shakawe, George, Maun, Mahikeng, tion of the average yield at any point in the study area by Wonderboom) after year 2010. One will see in Section 3.3 that subtracting annual dew yields between years 2020 and 2011. the year 2010 is also the year where rainfalls significantly Figure 3 shows the difference Δhd = hd (2020) – hd (2011). One decrease. sees that the evolution is different according to the locations. 404 Mapping past, present and future dew and rain water resources for biocrust evolution in southern Africa –1 Although dew decreases in two places where it was the most but with lower rainfall (285 mm year with a mean of 23.8 –1 abundant (SW and NE to a lesser extent), it increases in the mm month ). NW (Ondangwa, Eros) where dew was the lowest. A noticeable One notes a marked decrease in precipitation during the 20 increase is seen in N (Maun, Shakawe) and SE regions (Bram years period, all sites show α (hr) < –0.2, particularly in Eros Fischer). One notes that the biocrust sites are mostly located in and Ondangwa in Namibia, the 4 cities of Bostwana, and regions of null or moderate dew decrease. George and Bram Fisher in South Africa. Coastal sites in Namibia (Oranjemund, Luderitz, Swakopmund and Walvis 3.3 Rainfall Bay) show a smaller decrease (α (h ) ≈ 0). When looking at 3.3.1 Data description Fig. SM1 in Supplementary Materials (summed values of h ), one realizes that the main change in rainfalls occurred in 2010. Table 2 and Fig. 4 present annual and monthly mean, min It is from this year that a gradual change in rain can be ob- and max rainfall extracted from Infoclimat database (2021) for served. the studied period (sites: See Table 1). From a general point of The rainfall repartition presented in Table 2 is confirmed by view, rain decreases towards W and N. As described below, the Kriging map obtained for the annual mean rainfall (Fig. 4a). cities located at the Namib Desert exhibit lower rain precipita- Rainfall increases markedly from west to east (0–200 mm at the tions: 13.4 mm in Swakopmund and Walvis Bay (i.e. 1% of Atlantic coast to 600 to 700 measured at the south-east of South rainfall events by year) and in a lesser extent, Oranjemund with Africa). The same trend is observed with the monthly mean and a mean annual rainfall of about 42 mm (i.e. 5% of rainfall maximum rainfall volumes (Figs. 4b, c). The monthly average events by year). In these areas, precipitations are very erratic, varies from 0 to 20 mm (W) to 50 to 60 mm (SE). with no rain for several months and few intense precipitations events. In the inland, rainfall is slightly more abundant with 3.3.2 Evolution map annual averages of 115, 189 and 306 mm for Keetmanshoop, Ondangwa and Eros, respectively. Although these areas can By subtracting the precipitation values between years 2020 exhibit months without any rain, the monthly averages are and 2011 one can map (Fig. 5) the difference Δhr = hr (2020)– greater than 10 mm. However, one notes that less than 11% of hr (2011). Although the mean precipitation decreases, the evolu- the days of the year are rainy days (10.9%, 5.3% and 3.7% in tion is different depending on the locations. Rain mainly de- Eros, Ondangwa and Keetmanshoop, respectively). creases in the north regions (Maun, Shakawe, Eros), where dew For Botswana, the situation is more homogenous, with a was seen to increase during the same time period (Fig. 3). A mean rainfall of 463.2 mm observed in the four cities of Gabo- small zone in south west (Cape Town, Oranjemund) exhibits a rone, Maun, Francistown and Shakawe. With one or two precipitation increase. It is worthy to note that the biocrust zones months during the year without rain, this region present mean are mostly in the regions that experienced a decrease in rain. regular monthly rainfall of about 39 mm, with 13.4% of the days being rainy. 3.4 Correlation between dew and rain yields South Africa exhibits a contrasted behavior. The regions lo- cated along the ocean in the south and south east of the country The occurrence of dew is related to the presence of have heavy rainfall with annual amounts greater than 500 mm atmospheric high humidity. Some correlations therefore exist (Mahikeng, Cape Town, George, Port Elizabeth, Bram Fischer, between the frequency and amplitude of rain and the amplitude Wonderboom), with up to 715 mm in George (18–31% of the of dew yields. Two kinds of correlation can occur, a temporal year are rainy days). Monthly averages are important with a correlation, where dew forms after rain events, which have mean of about 49.6 mm (23.5% rainy days in the year). increased the atmosphere RH, and an amplitude correlation. Upington is an exception, located further west of the country, Both correlations are studied in the following. Table 2. Mean, minimum and maximum yearly (Hr) and monthly (hr) rainfall calculated from meteorological from 2001 to 2020 are fitted to Eq. (5) with free parameters α = dh / dt and h . r r r,0 –1 H (mm yr ) h (mm) year r r α h r r,0 Site frequency –1 (mm month ) (mm) Mean Min Max Mean Min Max (%) Swakopmund 13.4 0.0 56.0 1.1 0.0 41.2 –0.005 1.5 0.9 Walvis Bay 13.4 0.0 56.0 1.1 0.0 41.2 –0.005 1.5 0.9 Luderitz 18.6 1.0 83.5 12.4 0.0 64.1 –0.024 3.2 1.8 Ondangwa 189.4 6.6 453.0 15.8 0.0 155.0 –0.283 32.9 5.3 Oranjemund 42.2 7.0 225.8 3.5 0.0 115.6 –0.030 6.4 5.0 Keetmanshoop 115.7 20.8 278.4 9.6 0.0 145.1 –0.044 11.0 3.7 Cape Town 542.1 249.0 888.8 45.2 0.0 238.0 –0.148 57.0 24.8 Upington 285.1 53.0 518.4 23.8 0.0 261.4 –0.167 38.3 10.4 Shakawe 423.5 8.4 1072.3 35.3 0.0 447.1 –0.493 82.8 13.0 George 715.4 333.0 1223.7 59.6 0.0 290.5 –0.260 79.7 30.7 Maun 482.8 20.0 1115.9 40.2 0.0 375.3 –0.468 79.8 14.9 Mahikeng 582.8 182.0 1158.1 48.6 0.0 320.3 –0.135 55.5 19.7 Port Elizabeth 641.8 308.0 1103.8 53.5 0.0 235.5 –0.171 64.2 26.8 Gaborone 464.3 80.2 1023.3 38.7 0.0 372.5 –0.374 68.0 11.9 Bram Fischer 590.0 160.0 1190.0 49.2 0.0 274.7 –0.253 68.8 20.2 Francistown 482.3 46.2 1199.9 40.2 0.0 423.3 –0.342 66.2 13.6 Wonderboom 497.5 123.0 769.9 41.5 0.0 183.6 –0.095 49.9 18.5 405 Marc Muselli, Daniel Beysens Fig. 4. Mean rainfalls (mm) during the period 2001–2020. (a) Mean annual rainfall. (b) Mean monthly rainfall. (c) Maximum monthly rainfall. Red letters: Measurement sites (see Table 1); circles: biocrust sites according to Chen et al. (2020); right cross: Gobabeb site studied by Henschel et al. (2007) and Soderberg (2010); inclined cross: Potchefstroom site studied by Baier (1966). 3.4.1 Temporal correlation The temporal correlation between rainfall and dew yield is evaluated by a correlation coefficient r between the daily rain- fall, hr (t), and the time-shifted daily dew yield, hd (t+τ), esti- mated at the same location. The delay time τ corresponds to the previous and next days of time t and is counted in days in the interval [–31, +31]. The covariance between hd (t+τ) and hr (t) is calculated as: Ch t , h t+=ττ h t −h h t+ −h (6)  () ( ) () () ()() rd  r,, j r dj d  j =1 With σσ , the rain and dew standard deviation, respec- hh rd tively, one infers the correlation coefficient: Ch t , h t + τ ( ) ( )  rd rh ()t , h (t+= τ ) (7) rd  σσ hh rd Fig. 5. Difference between 2020 and 2011 of the annual rainfalls Considering that –1< r < 1, a negative correlation leads to an (mm). Red letters: Measurement sites (see Table 1); circles: opposite evolution of hr and hd, a positive correlation corre- biocrust sites from Chen et al. (2020); right cross: Gobabeb site studied by Henschel et al. (2007) and Soderberg (2010); inclined sponds to the two variables moving in the same trend and cross: Potchefstroom site studied by Baier (1966). r → 0 means that both variables are not correlated. 406 Mapping past, present and future dew and rain water resources for biocrust evolution in southern Africa The r correlation plots for each meteorological site accord- (iii) For τ > 0, some correlation can be observed for τ ≤ 3 ing to the three N scenarii are reported in Fig. 6. One observes days. For the Eros and Keetmanshop sites, r = 0.29 (N = 3) and the following: r = 0.18 (N = 1). For Mahikeng and Upington, r = 0.12 (N = 1) (i) For τ < 0, no correlations between dew and rain ampli- and r = 0.13 (N = 0). To a lesser extent, for Bram Fischer tudes are observed (mostly r < 0.05). It means that a rain event r = 0.097 for N = 1. These values thus indicate a weak but real at a given day does not explain dew events a few days earlier. positive correlation between rain and dew events. It means that, (ii) For τ = 0, all curves present negative values for r, with due to the increase of atmosphere humidity after rain events, dew events are more likely to be observed between one to three amplitude in the range between –0.3 and 0.1. This is due to the days after rainfalls. fact that, in the calculation of the dew yields in Section 2.1, one had to discard the days with rain. Fig. 6. Daily correlation coefficients rh (t ) , h (t + τ ) for time τ  −− 31 + 31 days. For stations with incomplete cloud cover data, the [ ] rd  curves are presented assuming N = 0 (blue), N = 1 (red) and N = 3 (grey). 407 Marc Muselli, Daniel Beysens The correlation dew-rain is most noticeable (Ondangwa, 400 12000 Eros, Keetmanshop; Upington, Mahikeng, Bram Fisher) when the distance from the ocean increases, the atmosphere RH then 10000 decreases (see Fig. 2d). In contrast, for stations close to the Rain C coast in arid climate (distance < 15 km) and with low annual Dew C 200 6000 rainfall (Hr < 50 mm) but large RH, such as Luderitz, Oran- Rain U jemund, Swakopmund and Walvis Bay, the correlation is very Dew U low regardless of the τ value. For the cities of Cape Town, Port Elizabeth and George, presenting a more temperate climate, the 2000 correlation shows at most a weak increase for τ < 4 to 5 days 0 0 (with r < 0.1). All these sites have an altitude below 200 m. Whatever is the N scenario, for altitudes between 800 m and 1700 m asl and > 200 km away from the ocean, the correlation Date is clearer with values of r showing a steady increase at Eros (1700 m asl, 266 km from the ocean), Keetmanshoop (1069 m 0.04 asl, 285 km from the ocean). Ondangwa (1099 m asl, 385 km from the ocean) and Bram Fischer (1349 m asl, 418 km from 0.035 the ocean) show a correlation with r > 0.1, respectively for τ = 0.03 2 and 3. For the other mountainous stations, the correlation Cape Town coefficients exhibit values that does not exceed 0.1, with τ = 5 0.025 for Gaborone (r = 0.0532) or τ = 3 for Maun (r = 0.0665). 0.02 3.4.2 Summed dew and rain yields 0.015 Upington 0.01 One now investigates the correlation between the cumulative 0.005 dew and rain monthly yields, sumhh = dt and () dd  0 0 04/2001 01/2004 10/2006 07/2009 04/2012 12/2014 09/2017 06/2020 Date sum()hh = dt , respectively, with t0 the starting time (see rr Table 1). Each data point will thus correspond to a monthly Fig. 7. Two typical evolutions (Upington U and Cape Town C mean value. For each month, a ratio at is calculated: sites) of dew and rain summed yields in the studied period (2001– ( ) 2020). The vertical dotted line corresponds to year 2010 where rainfalls begin to significantly decrease. (a) sum (hd) and sum(hr)  sum h ( )  with N = 0 missing data scenario (see text and Table 1). (b) Ratio at = (8) ()  sum h () a(t) = [sum(h )] / [sum(h )] . The horizontal straight lines are fits to d t r t  r a(t) = a0 = constant. In Fig. 7a the sum h , the sum ( h ) and their ratio a(t) ( ) d r Table 3. Ratio dew/rain summed amplitudes a (Eq. 9) according to for two sites (Upington and Cape Town sites) are reported (at different N assumptions for the missing data (see text and Table 1). small times the dispersion is large because the smoothing effect of the summation is still weak). In Cape Town, both rain and Site a (N = 0) a (N = 1) a (N = 3) 0 0 0 dew amounts are nearly linear during the research period, with Swakopmund 2.384 1.793 0.792 a decrease in rainfall rate after 2010 while the dew rate remains constant. In Upington, one observes a decrease in the rain Walvis Bay 2.444 1.841 0.832 amount and an increase in the dew amount after 2010. For sake Luderitz 1.154 0.940 0.569 of comparison in the whole time period, the data (Fig. 7b) can Ondangwa 0.023 0.016 0.006 be fitted to a mean constant value Oranjemund 0.858 0.651 0.282 a(t) = a (9) Eros 0.014 0.011 0.006 Keetmanshoop 0.020 0.014 0.006 The values of a according to the three N scenarios are Cape Town 0.028 0.028 0.028 summarized in Table 3. Taking into account all stations, the Upington 0.017 0.015 0.012 parameter a shows a large variability: a = 0.4 ± 0.8 (N = 0), Shakawe 0.011 0.011 0.011 a ± a ± = 0.3 0.6 (N = 1) and = 0.15 0.27 (N = 3). This 0 0 George 0.031 0.027 0.024 variability is due to the small number and erratic character of Maun 0.007 0.007 0.007 the precipitations in arid areas. When the very small quantities Mahikeng 0.013 0.011 0.007 of rain at these sites (Namib Desert: Oranjemund, Luderitz, Swakopmund and Walvis Bay) are removed, the variability of Port Elizabeth 0.026 0.026 0.026 values becomes much smaller ( a = 0.022 ± 0.008 (N = 0), 0 Gaborone 0.028 0.028 0.028 a = 0.020 ± 0.009 (N = 1) and a = 0.017 ± 0.011 (N = 3)). Bram Fischer 0.034 0.032 0.029 0 0 Francistown 0.018 0.018 0.018 The parameter a is mapped by the Kriging method in Fig. 8. Wonderboom 0.034 0.034 0.034 One can clearly observe the increasing importance of dew in a sum(h ) (mm) 01/2001 02/2002 03/2003 04/2004 05/2005 06/2006 07/2007 08/2008 09/2009 10/2010 11/2011 12/2012 01/2014 02/2015 03/2016 04/2017 05/2018 06/2019 07/2020 sum(h ) (mm) r Mapping past, present and future dew and rain water resources for biocrust evolution in southern Africa the total precipitations along the Namibian coast and more 3.5 Time period of events generally the dependence of a on longitude. It corroborates the fact that the distance from the ocean, which controls the atmos- Because the frequency or time period between rain events is phere RH (see Fig. 2), is the important parameter for the also an important parameter, which in itself can control the formation of dew. Toward the west, dew increases (Fig. 2) and biocrust growth, we investigate below this parameter for rain rain decreases (Fig. 4), leading to an increase in a. only, dew only and dew plus rain. For that purpose, one consid- The variation of the ratio a between 2020 and 2011 is ers the histogram of rain, dew and rain plus dew events (Fig. 10) reported in Fig. 9. One verifies the general increase of the where two important parameters can be extracted, the mean contribution of dew with respect to rain, especially towards time period between events, θ (in days) and the maximum time west. period, θM (in days). N = 0 N = 1 N = 3 Fig. 8. Map of ratio a0 corresponding to the average of a = sum(dew)/sum(rain) (Eqs. 8, 9) for the period 2001–2020 and three scenarios for missing N data (see text and Table 1). Letters: meteo sites; circles: biocrust sites according to Chen et al. (2020); right cross: Gobabeb site studied by Henschel et al. (2007) and Soderberg (2010); inclined cross: Potchefstroom site studied by Baier (1966). N = 0 N = 1 N = 3 Fig. 9. Variation between 2020 and 2011 of the ratio a0 = sum(dew)/sum(rain), corresponding to 3 scenarios for missing N data (see text and Table 1). Letters: meteo sites; circles: biocrust sites according to Chen et al. (2020); right cross: Gobabeb site studied by Henschel et al. (2007) and Soderberg (2010); inclined cross: Potchefstroom site studied by Baier (1966). Fig. 10. Typical histograms of time period θ (day) beetween (a) rain events, (b) dew events (c) rain and dew events. θ is the mean time and θ is the maximum time. Note that some dew or rain events can disappear in the histogram dew + rain because dew or rain events occur during the dew or rain time periods. 409 Marc Muselli, Daniel Beysens which can reach two orders of magnitudes. It results from the The evolution of θ and θ can be then considered (Fig. 0 M above observations that the dew events will determine the behav- SM2) and maps of mean values can be drawn for the consid- ior of the dew + rain time period (see Fig. SM2, Figs. 11–12). ered period (Fig. 11), with the difference between 2011 and When comparing the maps of dew and rain mean annual 2020 values (Fig. 12). Some curves are interrupted due to the times (Fig. 11) and dew and rain amplitudes (Figs. 2 and 4), lack of data. one observes a strong correlation between the zones of large One first notes from Figs. 10 and SM2 (in Supplementary Ma- times and low yield, and short times and high yield. This simp- terials) that the number of events is larger for dew than for rain. ly means that large water yields correspond to frequent dew or In addition, the timescale for mean and maximum time period rain events. between events is much larger for rain than for dew, a difference c d Fig. 11. Annual mean in the period 2001–2020 of the maximum time θ (day) (left column) and mean time θ (day) (right column). (a), (b): M 0 Rain; (c), (d): Dew; (e), (f): Rain+dew. Red letters: Measurement sites (see Table 1); circles: biocrust sites according to Chen et al. (2020); right cross: Gobabeb site studied by Henschel et al. (2007) and Soderberg (2010); inclined cross: Potchefstroom site studied by Baier (1966). 410 Mapping past, present and future dew and rain water resources for biocrust evolution in southern Africa Fig. 12. Difference between 2020 and 2011 of the maximum time θM (left column, day) and mean time θ0 (right column, day). (a), (b): Rain; (c), (d): Dew; (e), (f): Rain+dew. Red letters: Measurement sites (see Table 1); circles: biocrust sites from Chen et al. (2020); right cross: Gobabeb site studied by Henschel et al. (2007) and Soderberg (2010); inclined cross: Potchefstroom site studied by Baier (1966). The evolution of the mean and maximum time period between tively similar to the evolution of the rain and dew amplitudes 2001 and 2020 (Fig. SM2) show that mean and maximum time (Figs. 3 and 5). The inverse evolution of rain + dew times ra- periods evolve about the same way. The times keep nearly ther follows the dew evolution, as expected from the fact noted constant over the whole period for dew, noting some decrease above that the dew events mostly determine the behavior of the after 2010. Dew frequency is well correlated with the dew yield dew + rain times. amplitude, which remains constant or weakly increases in the same period (Fig. SM1 in Supplementary Materials). In contrast, 4 DISCUSSION AND RELATION WITH BIOCRUST for rain, while the times keep constant between 2001 and 2010, 4.1 Dew height dependence the times increase after 2010. This evolution corresponds well with the decrease of rain amplitude (Fig. SM1). Biocrust forms at the ground level while the calculation of The maps of evolution for the period 2011–2020 concerning Section 2.1 deals with a 30° tilted condenser at 1 m off the the differences in rain, dew and rain + dew times are reported in ground. Dew condensation can vary for three reasons. (i) RH Fig. 12. The evolution of mean and maximum times are qualita- can be height dependent. This is the case if wind speed is near 411 Marc Muselli, Daniel Beysens zero and soil is wet, for instance after a rain event. (ii) Air flow diminution of rainfall precipitations. On the Ghaap plateau in depends on height, and then, the heat and mass exchange with west center of South Africa, oscillations of rain precipitations the surrounding air. The variation of air flow velocity is known have been already noted by Tfwala et al. (2018) by analyzing to follow a log dependence above a roughness length z (see interannual rainfall variability on the Ghaap plateau. The cycles Section 2.3) where air flow velocity is zero. In addition to the last about 18–22 years in Postmarburg and between 12 and 16 forced air flow induced by wind, there exists a natural convec- years in Douglas. Another analysis of rainfall in South Africa tion induced by the substrate temperature colder than ambient by Zvarevashe at al. (2018) also concluded to quasi-decadal –1 air, with typical velocity 0.6 m s (Beysens et al., 2005; Clus et oscillations. The question whether the decrease we observed al., 2009). The log dependence of the windspeed and the pres- since 2010 is related to these oscillations or to the global ence of natural convection make the heat exchange coefficient climate change remains thus open. and then the mass diffusion coefficient, which determines the condensation yield, depend weakly of windspeed for values 4.4 Water availability and biocrust distribution –1 below ∼ 1 m s (measured at the standard height of 10 m). It As outlined in the Introduction, the amount of rain and dew results a weak dependence of condensation with height for such are considered as the main factors which influence the growth windspeeds, making the calculation of Section 2.1 valid at the of biocrust (see e.g. Kidron and Kronenfeld, 2020; Li et al., ground level. 2021a, b; Ouyang et al.; 2017; Pan et al., 2010; Zhuang and For larger windspeeds, the heat exchange coefficients will be Zhao, 2017). However, the frequency of rain events (longest larger, decreasing the dew yield. The latter will be then larger at period of drought) is the main factor according to Büdel et al. the ground level and the calculation of Section 2.1 will be a (2009). Although there are no studies concerning the effect of conservative value. frequency of dew events, one can reasonably assume that this 4.2 Comparison with direct dew yield measurements parameter also matters. Frequency of events and their amplitude are strongly corre- lated (see Section 3.5), the regions of large dew or rain ampli- The calculated dew yields can be compared with previous tudes corresponding to the regions of small dew or rain time works available in the literature. Baier (1966) reported dew and periods. Both criteria (amplitude, frequency) should thus corre- rainfall measurements from a weather station set at spond in the studied regions to the same characteristics favoring Potchefstroom (inclined cross in Fig. 2), located in the vast biocrust growth. interior plateau of South Africa (26°44’ S, 27°05’ E, 1352 m asl), The evolution between 2001 and 2020 is seen to exhibit two about 160 km from the Wonderboom site. During the period regimes, one from 2001 to 2010, where all parameters (dew and 1957–1958, the annual percentage of dew days was 45.7% (Won- rain amplitude, dew and rain frequency) keep nearly constant. derboom: 65.5%) with a mean annual dew amount of 12.6 mm The second regime, from 2010 to 2020, corresponds to a neat (Wonderboom: 19.9 mm). The values in Wonderboom are slight- decrease of rain amplitude and frequency of events, while dew ly larger, but the measurement time was earlier and we will see in the next Section that the general tendency is a positive dew amplitude and frequency either keeps constant or slightly in- yield evolution. crease. As far as rain is concerned, it should result in a decrease Dew collection were also carried out in 2006 by Henschel et of biocrust growth. However, dew yield is nearly constant or al. (2007) at Gobabeb (Namib Desert, 23°33.704 S, 15°02.466 E, increases after 2010. We are not aware of drastic changes in the distribution of biomass of biocrusts during the 2001–2020 right cross in Fig. 2) in Namibia's Central Namib Desert, situated period. This may be attributed to the increase of dew amplitude about 84 km from Walvis Bay and 110 km from Shakopmund. and frequency, which should act to compensate for the decrease The site elevation is 406 m. Only a few data were collected on a in rain precipitation. specially-designed 1 m passive dew collector. In July 2006, 3.3 mm of dew water was collected (12 dew days), 1.2 mm in Au- 5 CONCLUSION AND TRENDS FOR THE FUTURE gust (10 dew days), and 1.5 mm in September (10 dew days). Meteo data at Walvis Bay and Shakopmund are, however, avail- The determination of dew yield using a physical model and able only between 2010 and 2020. In these cities, the calculated rainfall data from 18 meteorological stations in Namibia, annual mean in July, August and September are nearly the same: 2.6 mm (July), 2.2 mm (August) and 2.2 mm (September) (N = Botswana and South Africa in the period 2001–2020 allow 0), 1.2 mm, 1.8 mm and 1.7 mm (N = 1) and 0.7 mm, 0.9 mm clear tendencies to be evaluated. Dew decreases from the East, and 0.9 mm (N = 3). Although not determined at the same dates, South, West coasts following the decrease in RH decrease, and these values compare relatively well with the above measured rainfalls diminish toward the West and North. A noticeable decrease in rain precipitations after 2010 and a corresponding values of 3.3 mm (July), 1.2 (August) and 1.5 mm (September). rise in dew yield are noted. It results in a steady increase of dew Between July 2008 and June 2009, Soderberg (2010) meas- contribution with respect to rain after 2010. In addition, a clear ured a greater amount of dew at Gobabeb, with 143 yearly dew increase in dew for three days in average after rainfall is events. The corresponding volume was 12.3 mm, which com- observed in the arid regions where the humidity is low. These pares relatively well with the Walvis Bay and Shakopmund results are corroborated with the frequency of dew and data for the same year: 21 mm (N = 0), 15.8 mm (N = 1), 7 mm rain events, which are closely correlated with dew and rain (N = 3). yields. The effect on biocrust is to show zones with less rain but 4.3 Variation in rain precipitation with increasing dew water. As far as rain is concerned, one As mentioned in Section 3.3, we observed a decrease of therefore should expect a decrease of biocrust growth. Howev- precipitation from west to east. All sites present a negative er, dew yield is nearly constant or even increases after 2010, variation in rain precipitation during 2001 to 2020. In which could possibly compensate the rain decrease as we are not aware of drastic changes in the distribution of biomass of particular, the decrease in precipitation is quite noticeable from biocrusts during the 2001–2020 period. 2010. In Namibia Lu et al. 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Received 20 June 2021 Accepted 1 October 2021 414 Mapping past, present and future dew and rain water resources for biocrust evolution in southern Africa –1 Appendix 1 – Dew yield calculation the wind-speed (V, m s ) at 10 meters of the ground, recorded every Δt = 1h., we compute an hourly yield h (mm) corre- We give below in Table SM1 an example of determination sponding to evaporation (h < 0) or condensation (h > 0) events. i i of dew yield from Section 2.1. The model (Eq. 2) is applied to By discarding evaporation (hi < 0) and rain events, the cumula- one night (March 21–22, 2010) in Cape Town (South Africa). tive dew yield h for each night is computed. For the studied Considering the sky cloud cover (N, oktas), the air (Ta, °C) and night, h = 0.185 mm. dew (Td, °C) temperatures, the relative humidity (RH, %) and Table SM1. Exemple of calculation of dew yields from meteorological data. Date Hour N V T RH T T –T h h > 0 sum(h ) a d d a i i i (dd/mm/aaaa) (hh:mm) (oktas) (m/s) (°C) (%) (°C) (°C) (mm) (mm) (mm) 21/03/2010 12:00 5 6.1 22 69 16 –6 –0.030 0.000 0.000 21/03/2010 13:00 5 7.2 23 65 16 –7 –0.035 0.000 0.000 21/03/2010 14:00 3 7.8 22 69 16 –6 –0.030 0.000 0.000 21/03/2010 15:00 1 7.8 22 69 16 –6 –0.030 0.000 0.000 21/03/2010 16:00 1 6.1 22 69 16 –6 –0.030 0.000 0.000 21/03/2010 17:00 1 5.6 21 68 15 –6 –0.030 0.000 0.000 21/03/2010 18:00 1 4.7 19 83 16 –3 –0.015 0.000 0.000 21/03/2010 19:00 0 3.1 18 88 16 –2 0.014 0.014 0.014 21/03/2010 20:00 0 0.6 18 88 16 –2 0.014 0.014 0.027 21/03/2010 21:00 0 1.9 15 94 14 –1 0.019 0.019 0.046 21/03/2010 22:00 0 3.1 14 100 14 0 0.024 0.024 0.070 21/03/2010 23:00 0 3.1 17 88 15 –2 0.014 0.014 0.084 22/03/2010 00:00 0 3.1 17 88 15 –2 0.014 0.014 0.098 22/03/2010 01:00 0 3.1 17 94 16 –1 0.019 0.019 0.117 22/03/2010 02:00 0 4.2 17 94 16 –1 0.012 0.012 0.128 22/03/2010 03:00 0 5.3 17 100 17 0 0.000 0.000 0.128 22/03/2010 04:00 0 3.6 18 94 17 –1 0.018 0.018 0.146 22/03/2010 05:00 0 3.1 17 100 17 0 0.023 0.023 0.170 22/03/2010 06:00 1 3.6 17 94 16 –1 0.015 0.015 0.185 22/03/2010 07:00 1 4.7 18 88 16 –2 –0.010 0.000 0.185 22/03/2010 08:00 1 6.7 21 83 18 –3 –0.015 0.000 0.185 22/03/2010 09:00 1 7.8 24 69 18 –6 –0.030 0.000 0.185 22/03/2010 10:00 1 9.2 25 61 17 –8 –0.040 0.000 0.185 22/03/2010 11:00 1 9.2 26 57 17 –9 –0.045 0.000 0.185 22/03/2010 12:00 1 10.8 25 65 18 –7 –0.035 0.000 0.185 th Appendix 2 – Kriging method the i location, s the predicted location and p the number of measured data. Kriging is a stochastic spatial interpolation method that pre- With the Kriging method, the λ weighted coefficients are dicts the value of a natural phenomenon at non-sampled sites by not only based on the distance between the surveyed points and an unbiased, minimal variance linear combination of observa- the forecast location, but also on the general spatial organiza- tions of the phenomenon at nearby sites. The Kriging tool as- tion of the surveyed points. To use the spatial arrangement in sumes that the distance or direction between the sample points the weighing, the spatial autocorrelation is quantified. Thus, in reflects a spatial correlation that can explain the surface varia- ordinary Kriging, the weighting λ depends on the distance tions. The Kriging tool applies a mathematical function to all i points, or certain determined points, located within a specific from the forecast location and the spatial relationships between radius. It determines the output value of each location. the values recorded around it. The Kriging tool is particularly suitable for cases where it is The experimental semi-variogram can be estimated from known that there is a spatial correlation of distance or a direc- point pairs: tional deviation in the data. Kriging deduces, by weighting nh ( ) existing readings, the probable values of unmeasured locations. γˆhZ=−sZs+h ² () () ( )  ii  2nh () i =1 To calculate the interpolated data Zs() at a specific location s0, the general formula of ordinary Kriging (OK) method con- where nh=− Card s,/ s s s≈ h () {( ) } ij i j sists of a weighted sum of the data (Goovaerts, 1997): with “card” represents the number of elements for the given ˆ condition. Zs() = λ Zs( ) 0 ii Classically, estimated semi-variogram are fitted by a spheri- i =1 cal variogram model as proposed in previous studies on rainfall th Here Zs ( ) corresponds to the measured value at the i lo- spatial estimation (Bargaoui and Chebbi, 2009; Lepioufle et al., cation, λ the ponderation coefficient to determine and relate to 2012; Rahmawati, 2020; Van de Beek et al., 2012). 415 Marc Muselli, Daniel Beysens Supplementary Materials time θ (day) and the maximum time θ (day) between (a) rain 0 M (orange line), dew (blue short interrupted line) and rain plus We present below supplementary materials for additional dew events (green long interrupted line). calculated data. Table SM2 gives the correlation between the sky conditions Figure SM1 reports the evolution of the dew summed values and the cloud cover in oktas according to NOAA. sum(h ) (dew, mm, full blue line) and the rain summed values d Table SM3 reports the yearly (Hd) and monthly (hd) mean, sum(hr) (rain, mm, interrupted red line) for the studied sites. minimum and maximum dew yields calculated from meteoro- Figure SM2 is concerned with the evolution of the mean logical data. Fig. SM1. Evolution of the summed values sum(h ) (dew, mm, full blue line) and sum(h ) (rain, mm, interrupted red line) for the studied d r sites. The vertical interrupted line corresponds to a significant decrease of rainfall after 2010 with dew yield remaining constant or weakly increasing. 416 Mapping past, present and future dew and rain water resources for biocrust evolution in southern Africa 417 Marc Muselli, Daniel Beysens 418 Mapping past, present and future dew and rain water resources for biocrust evolution in southern Africa Fig. SM2. Evolution of mean time θ (day) and maximum time θ (day) between (a) rain (orange line), dew (blue short interrupted line) 0 M and rain plus dew events (green long interrupted line). Some curves are interrupted because data are missing. 419 Marc Muselli, Daniel Beysens Table SM2. Correlation between sky conditions and cloud cover according to NOAA’s national weather service glossary, 2021. The abbreviations for sky conditions are the following: CLR = Clear; FEW = few; SCT = Scattered; BKN = Broken; OVC = Overcast. Observation N (oktas) CLR 0 FEW 1 SCT 3 BKN 5 OVC 8 Table SM3. Yearly (Hd) and monthly (hd) mean, minimum and maximum dew yields calculated from meteorological data. The mean evo- lution data during from 2001 to 2020 are fitted to Eq. (5) with free parameters α = dh / dt and hd,0. Red values correspond to a decrease dd of dew yield evolution, blue values to an increase. Cloud coverage N is assumed to be 0, 1 or 3 oktas when cloud cover data are missing (see text and Table 1). year Hd (mm) hd (mm) N α hd,0 Site frequency –1 (oktas) (mm month ) (mm) Mean Min Max Mean Min Max (%) 0 37.7 31.2 45.5 3.1 0.0 6.8 –0.002 3.2 85.6 Swakopmund 1 28.4 22.9 34.6 2.4 0.0 5.4 –0.001 2.4 84.9 3 12.6 9.4 15.9 1.0 0.0 2.8 –0.001 1.1 79.1 0 38.2 31.7 46.1 3.2 0.0 6.9 –0.002 3.2 85.8 Walvis Bay 1 28.8 23.3 35.1 2.4 0.0 5.4 –0.001 2.4 85.0 3 12.8 9.6 16.1 1.0 0.0 2.9 –0.001 1.1 79.3 0 16.2 3.6 26.3 1.3 0.0 4.9 0.001 1.3 42.3 Luderitz 1 12.6 2.8 21.4 1.0 0.0 4.3 0.001 0.1 40.3 3 6.6 1.3 13.3 0.6 0.0 3.0 0.000 0.5 34.8 0 4.9 0.4 13.5 0.4 0.0 3.7 –0.004 0.6 25.3 Ondangwa 1 3.5 0.3 9.8 0.3 0.0 2.8 –0.003 0.5 22.0 3 1.4 0.1 3.8 0.1 0.0 1.2 –0.001 0.2 13.5 0 42.5 32.4 56.8 3.5 0.9 8.2 0.003 3.2 81.5 Oranjemund 1 32.8 23.9 45.2 2.7 0.5 6.8 0.003 2.4 80.4 3 15.4 9.6 24.3 1.3 0.2 4.1 0.003 1.0 70.6 0 4.6 1.4 8.9 0.4 0.0 2.6 –0.004 0.6 16.7 Eros 1 3.5 0.9 7.0 0.3 0.0 2.1 –0.003 0.5 14.6 3 1.9 0.3 3.8 0.2 0.0 1.1 –0.002 0.3 13.3 0 3.0 0.8 5.7 0.3 0.0 1.8 –0.003 0.5 18.4 Keetmanshoop 1 2.2 0.5 4.2 0.2 0.0 1.4 –0.002 0.3 15.3 3 0.9 0.2 2.0 0.1 0.0 0.8 –0.001 0.1 8.7 Cape Town – 18.3 8.9 24.1 1.5 0.0 5.1 0.000 1.6 58.2 0 5.5 0.4 13.8 0.5 0.0 2.9 0.000 0.5 27.0 Upington 1 5.1 0.4 13.2 0.4 0.0 2.8 0.000 0.4 26.6 3 4.5 0.4 12.4 0.4 0.0 2.6 0.001 0.3 25.7 Shakawe – 8.0 3.5 16.5 0.7 0.0 4.5 0.003 0.4 43.9 0 27.0 12.8 38.5 2.2 0.0 4.7 0.004 2.1 64.5 George 1 25.7 12.8 37.4 2.1 0.0 4.7 0.003 1.9 64.3 3 23.3 12.8 35.3 1.9 0.0 4.7 0.002 1.6 64.0 Maun – 6.9 1.8 18.0 0.6 0.0 4.9 0.003 0.3 40.3 0 9.8 0.1 21.7 0.8 0.0 4.7 0.003 0.6 37.6 Mahikeng 1 8.1 0.1 18.1 0.7 0.0 4.1 0.002 0.5 35.8 3 5.5 0.1 12.2 0.5 0.0 2.9 0.001 0.3 33.2 Port Elizabeth – 20.0 14.3 26.8 1.7 0.0 4.5 0.000 1.6 64.1 Gaborone – 16.2 6.6 26.0 1.4 0.0 5.9 –0.001 1.4 57.8 0 26.5 14.4 38.8 2.2 0.0 7.7 0.001 2.2 66.4 Bram Fischer 1 24.0 11.9 38.7 2.0 0.0 6.8 0.000 2.2 65.6 3 20.1 8.7 38.4 1.7 0.0 5.6 0.000 2.2 64.8 Francistown – 12.1 4.9 23.8 1.0 0.0 4.2 –0.004 1.4 58.3 Wonderboom – 19.9 8.0 27.4 1.7 0.0 5.0 0.000 1.7 65.5

Journal

Journal of Hydrology and Hydromechanicsde Gruyter

Published: Dec 1, 2021

Keywords: Biocrust; Dew and rain evolution; Dew/rain ratio; Dew/rain correlation; Southern Africa; Climate change

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