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Defining minimum runoff length allows for discriminating biocrusts and rainfall events

Defining minimum runoff length allows for discriminating biocrusts and rainfall events J. Hydrol. Hydromech., 69, 2021, 4, 387–399 ©2021. This is an open access article distributed DOI: 10.2478/johh-2021-0029 under the Creative Commons Attribution ISSN 1338-4333 NonCommercial-NoDerivatives 4.0 License Defining minimum runoff length allows for discriminating biocrusts and rainfall events 1* 2 3 1 4,5 Roberto Lázaro , Adolfo Calvo-Cases , Eva Arnau-Rosalén , Consuelo Rubio , David Fuentes , 1, 6 Clément López-Canfín Estación Experimental de Zonas Áridas (CSIC), Carretera Sacramento s/n, 04120 La Cañada, Almería, Spain. Inter-University Institute for Local Development (IIDL), Department of Geography, University of Valencia, Edifici d'Instituts, 4ª Planta C/ Serpis 29, 46022, València, Spain. Department of Natural Sciences, Manchester Metropolitan University, John Dalton Building E410a, Chester Street, Manchester M1 5GD, UK. Department of Ecology, University of Alicante, C/ de San Vicente del Raspeig, s/n, 03690 San Vicente del Raspeig, Alicante, Spain. Ecodrone Works, C/ Señores Maripino Rosello, 4, 03550, Sant Joan d’Alacant, Spain. Departamento de Física Aplicada, Universidad de Granada, Avenida Fuente Nueva s/n, 18071 Granada, Spain. Corresponding author. E-mail: lazaro@eeza.csic.es Abstract: The runoff coefficient (RC) is widely used despite requiring to know the effective contributing area, which cannot be known a priori. In a previous work, we defined runoff length (RL), which is difficult to measure. This work aimed to define the minimum RL (mRL), a quantitative and easy proxy of RL, for use in a pilot study on biocrusts in the Tabernas Desert, Spain. We show that RC decreases according to a hyperbola when the contributing area increases, the independent variable being the length of the effective contributing area and its coefficient involving the effects of rainfall and surface features and antecedent conditions. We defined the mRL as the length of the effective contributing area making RC = 1, which is calculated regardless of the area. We studied mRL from three biocrust types and 1411 events clustered in seven categories. The mRL increased with rain volume and intensity, catchment area and slope, whereas plant cover and biocrust succession (with one exception) had a negative effect. Depending on the plot, mRL reached up 3.3–4.0 m on cyanobacterial biocrust, 2.2–7.5 m on the most widespread lichens, and 1.0–1.5 m on late-successional lichens. We discuss the relationships of mRL with other runoff-related parameters. Keywords: Semiarid; Biological soil crust; Runoff connectivity; Length slope factor; Infiltration; Tabernas Desert. INTRODUCTION Non-concentrated runoff seems to form a continuous water sheet on the soil surface during rainfall, whereas infiltration Abundant evidence shows that runoff is highly dependent on occurs simultaneously in a spatially irregular manner dependent rainfall features (volume and intensity), surface hydrological on the distribution of soil features. However, although the water properties (vegetation, biocrust, litter, stones, and other soil sheet completely occupies a surface, runoff does not travel an surface components), soil characteristics (texture, porosity, and undefined length because there is evidence that RC considera- organic matter), previous soil conditions (antecedent soil bly decreases while the considered area increases (Kidron, moisture), and topography (slope angle and contributing area). 2011; Mayor et al., 2011; Xu et al., 2009). The farther a water To study and compare the effects of these multiple factors input occurs from a runoff collector, the lower the amount of controlling runoff, the runoff coefficient (RC) is a widely used that input is collected. According to Lázaro et al. (2015), runoff parameter. length (RL) is the length of the hillslope travelled by runoff; Nevertheless, using the RC, requires knowing the that is, for any point, RL is the maximum distance, in a straight line following the maximum slope line, from which the runoff contributing area. Closed runoff plots (surrounded by a wall delimiting the monitored drainage area) have been widely used comes. (RL is different from the length of the path travelled by under the assumption that the complete delimited area is the water, which depends on the surface microtopography). RL is effective drainage area. Because this assumption is unfounded important because it (i) contains some information on the hy- (Kidron and Yair, 1997; Kidron, 2011), delimiting an area does drological connectivity, because at least the drainage area de- not make sense and, open runoff plots are preferable because limited by RL is necessarily fully connected; (ii) enables effi- they do not alter the natural fluxes and prevent the relative cient comparisons of the hydrological properties of different exhaustion of sediments (Boix-Fayos et al., 2006). However, surface types, rainfall types, and minimum inter-event times using open runoff plots, we continue without knowing the (MITs), etc., at least because it allows for determining the effective contributing area, even if we topographically delimit drainage area by its length; (iii) provides information on the an area in situ, which would be the maximum possible sediment transport capacity; and (iv) seems to have potential to contributing area. Thus, we should assume that we never know enable predictions about runoff flow at a point as a function of a priori the real drainage area corresponding to a runoff rainfall. measurement nor, consequently, the real RC. Therefore, we However, because RL cannot be directly observed, the RL need an alternative parameter enabling characterisation of the concept is elusive. Little is known about the RL values in given hydrological behaviour. circumstances, although Agassi and Ben-Hur (1991) studied the 387 Roberto Lázaro, Adolfo Calvo-Cases, Eva Arnau-Rosalén, Consuelo Rubio, David Fuentes, Clément López-Canfín effect of slope length on infiltration and runoff. Puigdefábregas spiration is around 1600 mm, water deficit occurs every month, et al. (1999) and Arnau-Rosalén et al. (2008) suggested that the in particular during summer (June–September). Insolation is slope length travelled by runoff is often only a part of the over 3000 hours per year, and the average annual temperature is catchment length. This idea also underlies the work of 18 °C (Lázaro et al., 2004). The study area was the El Cautivo Puigdefábregas (2005), who stated that temporal variability of field site, within the Tabernas Desert. Although calcareous rainfall controls runoff re-infiltration and its decay with slope sandstones are locally abundant, Miocene soft marine marls length. Lázaro et al. (2015) experimentally determined RL on dominate the lithology and produce an extensive badlands biocrusts, although at only 1 m of spatial resolution. However, landscape and a complex geomorphology developed during the such experiments were logistically complex and time consum- Quaternary (Alexander et al., 1994; Alexander et al., 2008). ing. Here, we propose a high-resolution, quantitative subrogate The parent material is mainly composed of silt-size (>60%), of RL that is simple and easy to measure, using data from the gypsum-calcareous and siliceous particles; fine sand ranges same study area. from 20% to 35%, and clay ranges from 5% to 10%. (Cantón et Biocrusts are complex communities constituted by microor- al., 2003). El Cautivo includes a series of parallel catchments, ganisms, lichens, bryophytes, fungi, and algae inhabiting the with residual hanging pediments between some of them. A soil surface and within the upper soil centimetres. They are clear surface-type pattern exists. A third of the territory is bare widespread on a planetary scale (Büdel, 2003) at the sites and eroded; biocrust is the main cover in another third; and also where vascular plants are limited by climatic factors, and they occupies the plant interspaces in the rest (Cantón et al., 2004; play an important ecological role because they affect almost Lázaro et al., 2000; Lázaro et al., 2008). every ecological process (Belnap and Lange, 2003; Maestre et The biocrust types described by Lázaro et al. (2008) in this al., 2011; Webber et al., 2016). Chamizo et al. (2016) published study area were simplified to three for this research: (i) domi- a review on the biocrusts’ hydrological role. Biocrusts consti- nated by Cyanobacteria (Cyano); (ii) dominated by the lichens tute a good system model (Bowker et al., 2010; Maestre et al., Squamarina lentigera and/or Diploschistes diacapsis (Squam); 2016) as well as adequate surface cover to study runoff due to and (iii) characterized by the lichen Lepraria isidiata (Lepra). the existence of previous experimental studies in the same area The site of Cyano where the runoff plots were constructed has a (e.g., Chamizo et al., 2012a; Lázaro and Mora, 2014; Solé- mature, relatively rough cyanobacterial biocrust, including Benet et al., 1997). On the other hand, biocrusts develop in small pioneer lichens, such as Endocarpon pusillum, Fulgensia plant interspaces where vegetation cannot form a continuous desertorum, and Fulgensia poelti. This biocrust is the colo- layer (mostly in drylands), and they are considered runoff nizing one (beginning with a purely cyanobacterial biocrust) sources, providing water to the plant patches (Rodríguez- and is widespread in any orientation, constituting a matrix-like Caballero et al., 2014; 2018). Thus, knowing their RL would layer on which the other biocrust types successively develop provide insights to advance the current source–sink theory. when possible. In the sunniest non-eroded sites, Cyano is dom- The initial hypotheses were as follows: inant and almost permanent. Squam is the most widespread a) RL is often much shorter than the topographical lichen-dominated biocrust. It usually develops after Cyano, drainage area, which represents the historical maximum of RL. preferring the unaltered north-to-east hillslopes with low plant Kidron and Yair (1997), Puigdefábregas et al. (1999), and cover, and including numerous lichen species, such as Buellia Puigdefábregas (2005) and Arnau-Rosalén et al. (2008) already zoharyi, Fulgensia fulgida, Diploschistes ocellatus, and Psora made suggestions in this line. decipiens. Lepra biocrust is late successional and exclusive to b) RL widely varies across numerous factors, such as the the shadiest north-faced hillslopes, where it occupies the plant rainfall features (intensity, volume and timing), the surface interspaces. Lichen species such as Squamarina carthilaginea, characteristics (including vegetation, soil, topography, Xantoparmelia pokornyi, and Teloschistes lacunosus are char- biocrusts, and stoniness), and the antecedent soil moisture. acteristic of Lepra, as well as some mosses such as Grimmia Because runoff strongly depends on these factors (Castillo et pulvinata, Didymodon luridus, and Tortula revolvens. al., 2003; Le Bissonnais et al., 1995), we assume that RL will also depend on them. Runoff monitoring c) In the study area, RL will be centimetres long rather than metres long for most natural rainfall (Lázaro et al., 2015), Two open runoff plots and a rain gauge were installed in which very often has low intensity or small volume (Lázaro et each biocrust. The plots at Cyano were labelled C1 and C2, al., 2001). those of Squam S1 and S2, and those at Lepra L1 and L2. Their d) Biocrust will generally have high RC, but it will vary appearance is shown in Fig. 1. The available data cover approx- according to its species composition (Lázaro et al., 2015). imately 10 years (2005–2015). Each plot consists of a PVC The objectives of this work were (i) to define the minimum channel, normal to the line of maximum slope, collecting runoff RL (mRL) and propose it as a concrete, quantitative, and easy and driving the water to a tank at the bottom of the hillslope. proxy of RL, and (ii) to use mRL for a pilot study to show the The channels, covered with a lid to avoid direct rain, are em- effect of biocrust type and rainfall class on RL from open run- bedded into the soil, and the contact of its upslope edge with off plots. the soil was in situ plasticised by means of fiberglass and epoxy resin, warranting the transit of the runoff to the trough. Inside METHODS the tank is a non-purpose tipping-bucket mechanism (0.5 L in The study area and the runoff plots resolution) connected to an on–off Hobo Event data logger, like that of the rain-gauge (0.25 mm in resolution). The Tabernas Desert is a place in southeast Spain, in the Sorbas–Tabernas basin, surrounded by the Gador, Nevada, Definition and calculation of mRL Filabres, and Alhamilla Betic ranges. The first three of these ranges intercept most rainfall fronts, which come mainly from Because the effective contributing area is not known the west, explaining the annual precipitation of around 230 mm a priori, examining the way RC varies in relation to it becomes (Lázaro et al., 2001). Because the annual potential evapotran- essential. To conduct this theoretical examination, we used 388 Defining minimum runoff length allows for discriminating biocrusts and rainfall events three minimum inter-event times (MITs): 24, 12, and 1 hour, values that are larger than 1 simply mean that runoff comes constructing three datasets with 436, 593, and 1411 rainfall – from upslope of the length attributed to the drainage area. The runoff events, respectively. For every event and each plot, we larger than 1 the RC value is, the larger the mRL is in relation calculated four RC values by successively assuming different to the supposed length. As can be verified from Equation (1), lengths (1, 2, 3, and 4 m) for the effective contributing area. when RC = 1, x = a. Therefore, we can define the following: These hillslope lengths, multiplied by the width of the plot mRL = a = R / P × cw (4) (m) (L) (mm) (m) (length of the collector, 2.18 m except for L2, at 2.16 m) gave rise to four nested, rectangular, and progressively larger sup- Note that in Equation (4), only three known parameters in- posed drainage areas per event, generating four RC figures. tervene, and the contributing area does not. This procedure implies assuming that they were ideal smooth To show these hyperbolic relationships, we used Equation and homogeneous hillslopes. Our real plots only approximate (1) to plot the hyperbolas of the average (thus blurring the these conditions, but this preliminary assumption is useful to effect of the antecedent soil moisture) RC vs lengths succes- explain the concept and calculation of mRL. Next, we applied sively assumed for the contributing area, for one plot of each this approach to real data, examining the way RC varies when biocrust type and two different rainfall classes. Later, to explore successively larger portions of the real catchment are consid- the effect of rainfall type on runoff, we classified the rainfall ered effective contributing areas. events into seven categories: >0–1, >1–3, >3–5, >5–10, >10– As the width of the plot is assumed to remain constant for 20, >20–30, and >30 mm. Because most of the rainfall events any channel length, the assumption of a series of hillslope were small, we divided the group of events ≤5 mm into three lengths (for the supposed effective drainage area) increasing classes to avoid an extremely large lower class and to gain according to the series of natural numbers produces a series of resolution to establish the rainfall threshold generating runoff. nested areas, increasing in arithmetic progression. Because runoff must be divided by the area, while the plot length in- Analysis of mRL at El Cautivo field site throughout creases linearly, the corresponding RC potentially decreases because the value of a series of fractions with arithmetically biocrust types and rainfall events increasing denominators decreases according to a potential curve of exponent –1, forming a hyperbola. Thus, for any pair On natural hillslopes whose topography generates somewhat of runoff and precipitation values (i.e., for any rainfall or sur- irregular drainage areas, in such a way that a regular increment face type and any slope angle), the RCs generated by assuming in the length of the supposed effective catchment does not successively longer contributing areas always decrease accord- imply a regular increment in its area, the theoretical relationship in Equation (1) is only fulfilled in an approximate way and a ing to the following curve: potential curve must be fitted. –1 RC = a × x (1) To examine the variation of RC with the length of the sup- posed contributing area using real data from El Cautivo runoff where x is the length of the part of the hillslope that is assumed plots, we first determined the perimeter of the catchment of each to be the effective contributing area and a is a coefficient that plot. Then we calculated the successively larger real areas de- varies widely, because it involves the effects on runoff of the limited by successive 10-cm buffers in parallel to the trough. rainfall and surface characteristics, and can be experimentally To establish the catchment areas and soil surface compo- calculated. nents, a series of manual photogrammetric flights were carried Thus, although we cannot calculate RC, we can determine its out by means of a DJI Phantom 4 Pro drone carrying a high- distribution. Furthermore, for a rectangular plot, RC is as fol- resolution, 1-inch sensor (20 Mp). Images were taken at 3.5–5 lows: m above ground level, combining nadir and oblique images with an estimated overlap of 80 and 70% (forward and side, RC = R(L) / (P(mm) × cw(m) × x(m)) (2) respectively) to obtain an average of 596 images per experi- mental plot. Images were processed in Agisoft Metashape Pro where R is the runoff measured in litres, P is the measured (L) (mm) (Agisoft LLC, Russia). Resolution ranged from 0.95 to 1.13 precipitation in millimetres, cw(m) is the width of the collector –1 –1 mm pixel and 1.9 and 2.7 mm pixel for orthomosaics and the in metres, and x(m) is the hillslope length of the supposed effec- digital elevation model, respectively. tively contributing area in metres. Therefore, it is After removing most of the plants, using the Agisoft Metashape image classification software and then manually, the a = R(L) / P(mm) × cw(m) (3) digital terrain model was processed to identify the catchment areas draining to the collectors (Hydrology Tools, ArcMap 10.8). These curves relating RC with the length of the contributing Then, each catchment area was divided into parallel 10-cm area for any event of any surface type are determined by only bands, parallel to the runoff collector (Multi-ring Buffer, QGIS one parameter (a). Any value for length leads to a value for RC 3.14). From the digital terrain model, the average slope of each that exactly matches a point in the hyperbola. Because the catchment was also obtained (Zonal Statistics, ArcGis 10.8). hyperbola has an indefinite length, a length of contributing area Thus, every regular increase in slope length corresponds to a corresponding to RC = 1 always exists, independently from the different, but real, increase of contributing area. Then we calcu- surface and rain characteristics. As some infiltration always lated the RCs for every area (10 cm longer than the previous), occurs, the actual RL will be larger than the hillslope length plotted those RCs vs the hillslope length, and fitted a potential corresponding to RC = 1 is. Therefore, the hillslope length of curve. In a first step, we did this not for any concrete event but the supposed effectively contributing area corresponding to RC = 1 can be considered the minimum RL (mRL) for the for the average and for the maximum RCs of every rain type given set of circumstances (rainfall event, surface and anteced- and every biocrust type to verify the quality of the fittings and ent conditions) and enables an easy definition for mRL. This obtain a graphical reference of the mRL values. means that the minimum hillslope length travelled by runoff for We determined the cover of vascular plants, biocrusts, and a certain site and event is larger than the mRL. RC hyperbola bare soil in each plot by adding the segments occupied by every 389 Roberto Lázaro, Adolfo Calvo-Cases, Eva Arnau-Rosalén, Consuelo Rubio, David Fuentes, Clément López-Canfín C1 C2 S2 S1 L1 L2 Fig. 1. El Cautivo hillslope scale open runoff plots. surface type at 1 mm resolution in transects along the catch- and the covers of vascular plants in the catchment areas delim- ment area drawn on the plot orthophotomap (to avoid trampling ited by 1 m, 2 m, and 8 m upstream of the channel were also the plots). The length occupied by each type of coverage in initially considered as covariates. Instantaneous rain intensity relation to the total length of the transect was directly consid- was calculated for every rainfall record (rainfall volume input ered its cover percentage. divided by the difference between the time of that record and We used Equation (4) to calculate mRL directly for every the time of the previous), and the data used here were the aver- rain and runoff event of each MIT (24, 12 and 1 hour). We age and the maximum intensities for each event. Then, we carried out generalized linear modelling analyses to test for reduced the number of covariates, taking into account their differences in mRL according to two factors and their interac- interrelationships, the available statistical power, and the signif- tion: rain classes (seven categories) and biocrust types (three). icance levels that the covariates reached in preliminary, tenta- We explored the instantaneous rain intensity and the rain dura- tive analyses (see in Results). To perform these analyses, we tion as covariates; the volume of precipitation was not included selected a gamma data distribution and log as link function, due to its redundancy with the rain class factor. To account for including the records having mRL larger than zero, and used the differences among individual plots, catchment areas, slope Statistica 7.1 software (StatSoft, Hamburg, Germany). angles, the covers of vascular plants, biocrusts, and bare soil, 390 Defining minimum runoff length allows for discriminating biocrusts and rainfall events RESULTS Every pair of plots on the same kind of surface have a simi- Features of runoff plots and rainfall events lar hydrological behaviour (Fig. 2), except for Squam biocrust. The shape of the point clouds in Fig. 2, resembling a partially The characteristics of the runoff plots determined by analys- open “fan” and curved upwards, shows the increasing effect of ing the drone images are shown in Table 1. rain intensity and antecedent soil moisture as the precipitation The duration, volume, intensity, and number of events for volume increases. The amplitude of these “fans” shows the every rain type and every MIT are summarized in Table 2. variance due to the rainfall type and timing. Additionally, we The regression coefficient between runoff and rainfall was can obtain an idea about the effect of biocrust type on runoff by quite similar for the events from the three MITs in every plot comparing the scaling in the y-axes. and slightly higher for the 1-hour MIT (0.630 on average vs Rainfall volume to start runoff progressively increases 0.572 and 0.575 for the 24- and 12-hour MITs, respectively). through biocrust types; it is short at Cyano, medium at Squam, Thus, we show the analyses with the 1-hour MIT, which, and larger at Lepra. Considering all the plots and events of the moreover, produces the largest number of events. The larger 1-hour MIT, we found 2336 cases (sum of events including all maximum rain intensity belonged to event class 5 (although the the plots) with an mRL equal to zero and 21 with an mRL larg- average intensities were not very different among MITs). er than zero within the rainfall class 1. The same values were, The very large maximum intensity recorded in event class 1 respectively, 1029 and 70 for class 2; 305 and 121 for class 3; when we used MIT 1 lasted 5 seconds and did not generate 181 and 245 for class 4; 85 and 215 for class 5; 9 and 81 for runoff. class 6; and 3 and 33 for class 7. Table 1. Features of the runoff plots used at the El Cautivo field site. Biocrust types are described in the main text. Area is the contributing area according topography (m ). Length is the slope length of the area (m). Slope is the average slope angle (degrees). Aspect is the general orientation (degrees in eastward direction). Covers are given as %. Plant cover 1 m is the plant cover in the first meter upstream from the collector. Aspect Plant Biocrust Bare Plant Plot Biocrust Area Length Slope eastward cover cover cover cover 1m C1 Cyano 8.59 7.04 24.46 265 22.13 73.65 4.22 8.45 C2 Cyano 10.79 6.19 16.79 84 8.58 81.63 9.79 5.87 S1 Squam 19.15 13.64 33.18 7 27.04 70.20 2.76 14.24 S2 Squam 22.38 9.72 43.59 4 11.58 69.00 19.42 27.30 L1 Lepra 21.91 12.56 40.92 20 30.95 57.94 11.12 5.59 L2 Lepra 31.08 11.44 41.96 22 34.57 54.05 11.37 49.10 Table 2. Features of the rainfall events; averages from the three rain-gauges. Average and maximum duration are in days; average volume is rainfall in mm; average and maximum intensity are in mm/hour. *Remember that maximum intensity lasted only 5 seconds. 1 2 3 4 5 6 7 Rain class >0–1 mm >1–3 mm >3–5 mm >5–10 mm >10–20 mm >20–30 mm >30 mm number of events 199 72 31 42 52 21 19 average duration, days 0.33 0.65 0.80 1.18 1.33 1.73 2.68 maximum duration, days 3.26 4.16 3.25 8.93 4.60 4.66 6.86 MIT 24 h average volume, mm 0.32 1.72 3.63 6.58 13.13 23.31 39.07 average intensity, mm/h 5.75 0.64 0.40 0.85 0.96 1.22 1.21 maximum intensity, mm/h 542.99* 12.08 1.15 13.17 8.48 7.06 7.13 number of events 323 94 36 48 54 22 16 average duration, days 0.14 0.29 0.50 0.56 0.80 1.17 1.26 maximum duration, days 0.86 0.90 1.94 2.02 2.96 3.62 2.61 MIT 12 h average volume, mm 0.27 1.66 3.74 6.53 12.93 24.69 34.83 average intensity, mm/h 1.37 1.06 0.48 1.03 1.23 1.56 1.74 maximum intensity, mm/h 20.27 12.08 1.26 13.17 8.48 7.06 7.13 number of events 1014 184 71 71 50 15 6 average duration, days 0.02 0.06 0.10 0.16 0.25 0.30 0.39 maximum duration, days 0.12 0.27 0.34 0.41 0.76 0.74 0.68 MIT 1 h average volume, mm 0.22 1.64 3.62 6.76 13.38 23.55 36.16 average intensity, mm/h 1.57 2.33 2.73 3.07 3.67 5.51 4.61 maximum intensity, mm/h 20.27 18.41 19.44 18.61 40.88 20.12 9.16 391 Roberto Lázaro, Adolfo Calvo-Cases, Eva Arnau-Rosalén, Consuelo Rubio, David Fuentes, Clément López-Canfín Fig. 2. Runoff (y-axis in litres) vs rainfall (x-axis, mm). Data are the total of each event, using the 1411 events distinguished by the 1-hour MIT. Every graph shows the two plots of the same biocrust type. Graphs A, B, and C correspond to Cyano, Squam, and Lepra, respectively, and are presented in ascending successional order. Note that the scales of the y-axes are different. Fig. 3. Examples of hyperbolas relating to the RC with the length of the supposed effective contributing area. For each plot, we use the mean runoff and precipitation of all events of the rainfall classes 3 (>3–5 mm) and 5 (>10–20 mm), generated with the 1-hour MIT. For every pair of rain and runoff data points, we successively assumed four rectangular, nested, effective contributing areas having the length of the channel as width and 1, 2, 3, and 4 m as length. All hyperbolas are asymptotic with respect to the Y axis, thus, a length for the effective contributing area that makes RC = 1 always exists. A RC value > 1 or >> 1 indicates that the assumed length for the contributing area is less or much less than the real one. Theoretical curves of decrease of RC according to regular based in the maximum runoff peaks, the average runoff, or any increase of contributing area other runoff parameter. The maximum mRL (Fig. 4) was be- tween 3.3 and 4 m at Cyano, about 2.2 m at S1 (although it was The RC hyperbolas differed in the distance of the vertex about 7.5 m at S2), and between 1.0 and 1.5 m at Lepra. from the origin of coordinates, which vary according to surface Using the 12-hour MIT and 24-hour MIT, the number of types, topography, antecedent soil moisture, rainfall types, etc. events changes, as well as the proportion of events belonging to Fig. 3 shows some examples for theoretical regularly increasing every rainfall class. However, the goodness of fit and the gen- areas. Even for a surface with high infiltration (with the hyper- eral features of the results are practically the same as those bola vertex close to the coordinates’ origin), a positive slope shown in Fig. 4. length for which RC = 1 (an mRL value) always exists. Fig. 5 shows that runoff peaks were different in every bi- In these theoretical curves, the greater the MIT, the greater ocrust, as well as for every rain class. Note that the largest RCs the RCs and the further the hyperbola vertex were from the are produced by rain class 5. origin of the coordinates, because of the greater proportion of These graphs offer an understanding of the relationship be- large events (Table 2). tween RC and contributing area, verify the goodness of the fit, and provide a graphical value of mRL. Once a good fit was Goodness of fit of the real drainage areas to the theoretical established, we analysed mRL data calculated event by event hyperbolas by using Equation (4). When we used successive bands of the real catchment areas Analysis of mRL with regard to rainfall, surface and of every plot to exam the relationship between RC and increas- topography features ing contributing areas, the fit of the hyperbolas (Fig. 4) was very good, because the plots’ catchments are vaguely smooth The analyses showed significant differences in mRL accord- and rectangular, at least along the hillslope meters closer to the ing to all of the factors and included covariates. Rain duration and the cover of bare soil were removed because they were not channel. significant when analysed along with the other variables. The The abscissa corresponding to the point where the hyperbola biocrust cover was also removed because it shows a clear nega- crosses the value 1 of ordinates is the mRL. These curves show tive relationship (R = 0.86) with plant cover. The plant cover that for any surface and rainfall, maximum RCs are much larger within 1, 2 and 8 m upstream from the runoff collector, alt- than average. Therefore, for a case in which a curve refers to a hough often independent from the general plant cover, were set of events, it is crucial to specify whether the used mRL is 392 Defining minimum runoff length allows for discriminating biocrusts and rainfall events Fig. 4. Difference between the average and maximum runoff. Hyperbolas fitting the variation of RC when successively larger portions of the real topographic catchment of every plot, delimited by parallel lines spaced 10 cm from each other, are assumed to be the effective contributing areas. Data using the 1-hour MIT. All hyperbolas are asymptotic with respect to the Y axis, thus, a length for the effective contributing area that makes RC = 1 always exists. A RC value > 1 or >> 1 indicates that the assumed length for the contributing area is less or much less than the real one. Fig. 5. Graph A: Hyperbolas of RC vs contributing area for each plot using the maximum RC of the entire event series and the bands of the real topographical catchments. Graph B: Hyperbolas using the maximum RC of the event classes in the most responsive runoff plot (S2), and the bands of the real topographical catchments (R are the same for all the rain classes because all the curves refer to the same plot and to the same increments of contributing area). Both graphs used data from the 1-hour MIT. All hyperbolas are asymptotic with respect to the Y axis, thus, a length for the effective contributing area that makes RC = 1 always exists. A RC value > 1 or >> 1 indicates that the as- sumed length for the contributing area is less or much less than the real one. 393 Roberto Lázaro, Adolfo Calvo-Cases, Eva Arnau-Rosalén, Consuelo Rubio, David Fuentes, Clément López-Canfín also removed to gain statistical power and used in alternative An mRL threshold in at about 3 mm of rainfall has been found analyses instead of the general plant cover. Thus, the final (Fig. 6): At less than 3 mm of rainfall, the peaks of mRL never analysis included both factors (biocrust type and rain class) and reached 10 cm (runoff was rare in rain classes 1 and 2, but their interaction, three covariates to account for the features of sometimes it occurred; see above). every particular plot (catchment area, slope, and plant cover), The biocrust type significantly affected the mRL (Fig. 7A), and the rain intensity as an additional covariate, because it is and when we removed the data from plot S2, the mRL decreased poorly related to the rainfall volume. Table 3 summarizes the along biocrust succession (Fig. 7B). However, the features of results of the final analysis. S2, with much larger runoff due to other factors (such as larger The mRL consistently increases when rainfall increases, and bare soil area and slope angle), deform the relationship between the differences between rain classes are often significant. mRL and the successional sequence if S2 is included. Table 3. Significance of the effects of the different factors, interactions, and covariates on mRL, according to hypothesis testing using generalized linear modelling. Effect Degrees of Log- Chi- p freedom likelihood square Event class 6 –205.644 221.2202 0.000000 Biocrust type 2 –164.662 81.9652 0.000000 Event class × Biocrust type 12 –146.243 36.8361 0.000237 Rain intensity 1 –476.893 56.0725 0.000000 Catchment area 1 –464.168 25.4504 0.000000 Slope angle 1 –456.728 14.8815 0.000114 Plant cover 1 –316.254 280.9465 0.000000 bc Fig. 6. Average mRL for the sets of events in every rain class produced using an MIT of 1 hour, including the data from all the plots. Different letters on the boxes indicate significant differences. 1.8 0.8 1.6 0.7 a 1.4 0.6 1.2 0.5 1.0 0.4 mRL 0.8 0.3 0.6 0.2 0.4 0.1 0.2 Mean Mean±SE Mean±0.95 Conf. Interval Mean Mean±SE Mean±0.95 Conf. Interval 0.0 0.0 Cyano Squam Lepra Cyano Squam Lepra Biocrust type Biocrust type Fig. 7. Differences in mRL according to biocrust type. Graph A includes all the plots, and the differences are highly influenced by the larger runoff in plot S2. Graph B does not include the data from plot S2 and shows that infiltration increases along the ecological succes- sion. Different letters on the boxes indicate significant differences. mRL mRL Defining minimum runoff length allows for discriminating biocrusts and rainfall events S1 S2 mRL Mean; Whisker: Mean±SE -1 12 345 67 Event Class Fig. 8. Interaction between biocrust type and rain event class. Every line corresponds to a biocrust type, but for Squam the plots are shown separately because they behave quite differently. Except for plot S2, mRL decreases along biocrust succession. The threshold of mRL at 3 mm rainfall is distinguishable in this figure as well. The interaction between biocrust type and rain class is before reaching the collector. This threshold plot length is RL, a shown in Fig. 8. The larger the rainfall, the larger the difference concept providing a measurement of the decay of RC as the in mRL is among biocrusts. Biocrust type modulates the way in drainage area increases. Connectivity is usually larger, some- which the different rainfall classes affect runoff. However, the times drastically larger, than RL. difference is also due to the slope and other causes such as plant To explore and discuss the relationship of RL or mRL with and bare soil covers; the influence of plot S2 expanded the the length slope factor (LSF) or potential sediment transport range of mRL along the event classes in the Squam biocrust. index (Moore and Burch, 1986), a parameter derived from the Average rain intensity, contributing area and slope angle had digital elevation model, could be interesting. The LSF is a a positive significant effect on mRL, whereas plant cover had a surrogate that indicates the erosive potential of runoff, and its negative significant effect (Table 3). When we carried out the formula is LSF = (Xh / 72.6) , where Xh is the horizontal alternative analyses replacing plant cover successively by the length in meters of the slope and m is the exponent of the slope plant cover at 1, 2, or 8 m upstream of the channels, each cover variable, defined as m = ɛ / (1 + ɛ). The term ɛ relates to erosion showed a significant effect on mRL. in the furrows and between furrows and is defined as ɛ = 0.8 The number of events decreases when the MIT increases sin / 0.0896 × (3 × (sin ) + 0.56), where is the angle of and, whereas the duration of the events tends to increase expo- the slope (McCool et al., 1997; Zhang et al., 2017). RL and nentially when MIT increases, the rain intensity tends to de- mRL should relate closely to LSF because the (potential) crease potentially when MIT increases. However, the general- transport capacity of sediments depends on runoff. Interesting- ized-linear-model results show the same pattern with all the ly, LSF is a factor deduced from topography, but mRL is calcu- MITs, with all the considered factors, interactions, and covari- lated from runoff and precipitation from specific events. In ates of the final model being significant. reality, both concepts are independent and complementary approximations. As a first tentative hypothesis, if we replace DISCUSSION the slope length with the mRL in the LSF formula, the resulting RL and mRL potential sediment transport capacity would become actual capacity, that is, actual sediment transport if sediments are RL and mRL are different from hydrological connectivity. A available. This could be verified empirically, and if so, mRL stream or river can connect large distances; however, a certain could be highly useful for a predictive erosion model where concrete water volume usually does not cover all the connected sediment availability is not a limiting factor. distance because it stops at some point on the shore, infiltrates, As Lázaro et al (2015) discussed, the “flow length index” of evaporates, or is absorbed by plants. Similarly, when diffuse Mayor et al. (2008) is conceptually comparable to RL. Howev- surface runoff (not concentrated in rills) occurs, the entire er, it does not include the incoming rainfall. hillslope length can be hydrologically connected, but that does The slightly higher regression coefficient between runoff not necessarily mean that RL is the entire hillslope length. and rainfall for the 1-hour MIT we found agrees with the results (However, it is certain that all the space covered by RL is con- of Molina-Sanchís et al. (2016). nected.) If we progressively increase the length of the plot We believe that mRL is a proxy of RL with general validity. undergoing simulated rainfall, runoff volume increases until a By changing the rainfall or surface features, the parameter ‘a’of certain plot length (Lázaro et al., 2015) because, beyond that Equation (1) changes, but it does not change the concepts or length, all the water felt in the upper end of the plot infiltrates interpretations of the processes. The hyperbolic relationship we mRL Roberto Lázaro, Adolfo Calvo-Cases, Eva Arnau-Rosalén, Consuelo Rubio, David Fuentes, Clément López-Canfín found between RC and real drainage area length (Fig. 4) is 2007). Our result partly agreed with Belnap (2006), who found consistent with the potential decrease of RC experimentally two hydrological behaviours: Green algae and microfungi be- determined by Lázaro et al (2015). In the experiments, the have similarly to cyanobacteria, whereas bryophytes are similar curves fit worse because different plots (although close, homo- to lichens. geneous, and under the same simulated rainfall) represented the Because the development of some biocrust types takes long- different lengths. The goodness of the fits in Fig. 4, along with er than that of others, and eventually one type is replaced by a certain irregularity of the shapes and micro-reliefs of our real another (Lázaro et al., 2008), it is widely agreed that different drainage areas, show that our proposal is applicable in an ex- biocrust types can be understood as successional steps (Belnap tensive range of plots, because when we installed our plots in et al., 2006; Li et al., 2013; Rodríguez-Caballero et al., 2015), 2005, we did not look for ‘ideal-like’ hillslopes. although some scholars do not regard different crust types as being necessarily successional stages (Kidron, 2019). In our Runoff on biocrusts at the El Cautivo field site area, the succession begins from Cyano and progresses to Squam and finally to Lepra (Lázaro et al., 2008). However, As expected, the larger the rainfall, the larger the mRL. We succession shows different speeds at different habitats and can found occasional runoff even in rain classes 1 and 2, which stop at any point. It strongly depends on the microclimate, Rodríguez-Caballero et al. (2014) also found in the same study mainly on sun radiation and water availability. Where there are area. Despite an mRL value existing as long as the runoff is not conditions for development of lichens or mosses, Cyano can measurable, a clear threshold can be observed in the relation- be almost permanent on a human life timescale. ship between mRL and rainfall (Fig. 6). The way in which the Except for plot S2, our results show that infiltration tends to rain class affected the mRL depended often on the biocrust type increase along biocrust succession. This is consistent with our (Fig. 8). Lázaro et al. (2015) also observed that interaction: A previous experiments and with Gypser et al. (2016). Although threshold of runoff vs rainfall is associated with a different rain biocrusts are often considered runoff sources (Cantón et al., class depending on the biocrust type. 2002; Rodríguez-Caballero et al., 2018), their RC is generally The larger the rain intensity, the larger the mRL. This caused lower than that of bare soil with physical crust (Eldridge et al., that the rain class 5 gave rise to the largest runoff coefficients 2020) because biocrust succession progressively increases (Fig. 5B), despite classes 6 and 7 involving larger rainfall vol- water retention (Gypser et al., 2016) and soil moisture (Chami- umes, as the intensity of class 5 was clearly larger when using zo et al., 2013). This increase of infiltration along succession is MIT 1 (Table 2). This is consistent with what was previously due to multiple factors, including (i) the effect of pore clogging stated in the same study area, under natural rainfall (Rodríguez- increasing runoff in the early successional stages, favoured by Caballero et al., 2014) and rain simulations (Lázaro et al., cyanobacterial exopolysaccharides (Kidron et al., 1999); (ii) the 2015). The same was found in other locations (Guan and Cao, increase of surface roughness increasing infiltration as the 2019). succession progresses (Chamizo et al., 2010; Kidron, 2007; As expected, there were significant differences in mRL Rodríguez-Caballero et al., 2012); and (iii) the larger proportion among biocrust types. Except for the Squam biocrust, the dif- of mosses and vascular plants in the latest-successional biocrust ferences among plots belonging to the same biocrust type were (Lázaro et al., 2008), because mosses show larger infiltration much smaller than the differences among types (Fig. 2). The capacity than do lichens (Fischer et al., 2014). In addition, larger slope of plot C1 with regard to C2 was compensated by a plants, which develop progressively, are the main runoff sinks lower contributing area. The lower plant cover of plot L1, par- (Minea et al., 2018; Solé-Benet et al., 1997). Hydrological ticularly in the first meter upstream of the collector (Table 1), changes associated with successional stages have also been compensated for its smaller drainage area. However, the two found in more mesic and larger vegetation including biocrusts plots at the Squam biocrust behaved differently. Much larger (Lichner et al., 2012). runoff was consistently recorded for plot S2 during the sampled Comparable data on RL from other areas are scarce. Kidron period. It has larger slope, less plant cover, and much higher (2011) reported an average RL of 5.0 m, while Kidron and Yair cover of bare soil, with its upper part eroded (Table 1). The (1997) estimated a length of 7 to 10 m for the effective contrib- slope angle in S2 is 45º in the first 8 m upstream of the collec- uting area in the case of the peak runoff produced at the end of tor, which is relevant because the maximum recorded mRL was the heaviest storm, when the biocrust was already saturated, in shorter than 8 m. We did not find in the literature a slope their most responsive plot, which had only 10% of plant cover threshold beyond which runoff disproportionately increases. and a relatively smooth biocrust. This length is close ourmaxi- However, where soil is silty, runoff is larger on bare than on mum mRLvalue, which reached 7.5 m in our most responsive biocrusted soil (Wei et al., 2015; Xiao et al., 2019). Soil texture plot. seems determinant: In Tabernas’ silty soils, biocrusts often To our knowledge, this is the first study on the hydrological generate less runoff than bare soil, but in the sandy soils of the behaviour of the Lepra biocrust. Chamizo et al. (2012a; 2012b) Negev, biocrust shows threefold higher runoff than bare soil and Lázaro et al. (2015) did not include Lepra to avoid severe (Kidron, 1999). Chamizo et al. (2012a) and Lázaro et al. (2015) alterations, as its typical large slope angle generates significant also found significant differences in runoff between biocrust challenges in the experiments. This is interesting because Lepra types. Although cyanobacterial biocrusts tend to produce larger is the permanent biocrust community that occupies the plant mRL, Rodríguez-Caballero et al. (2013) and Chamizo et al. interspaces in non-eroded mature grassland or scrubland sites. (2012b) noted that the difference in runoff between cyanobacte- Furthermore, because the sites chosen for the Lepra plots have rial and lichenic biocrusts decreases to nothing as rainfall vol- relatively low grass cover, the runoff will be still lower in ma- ume increases. Our result is consistent with Kidron et al. ture grasslands. (2003), who found in Negev a substantial reduction in the RC The mRL is consistently lower in Lepra over time, despite from cyanobacterial to moss-dominated biocrust, explained by the slope, because of the greater plant cover (Minea et al., the lower amounts of extracellular polymeric substances and 2018) and number of small plant patches and annual plants. the higher roughness of moss-dominated biocrust. Small differ- First, there is a larger number of plant roots acting as preferen- ences in the micro-relief already affect the runoff (Kidron, tial infiltration routes; second, fine-grained plant patches are 396 Defining minimum runoff length allows for discriminating biocrusts and rainfall events more efficient in reducing runoff than the coarse-grained ones intensity), as well as those of the surface (biocrust type and (Bautista et al., 2007). In addition, soil porosity is larger under plant cover) and those of topography (contributing area and plants (Mora and Lázaro, 2014), and plants further increase slope angle), determined mRL. Different biocrusts had different infiltration by intercepting rainfall and producing stemflow mRLs and whereas rainfall, area, and slope had a positive (Jian et al., 2018). Furthermore, under alpha grass, biocrust relationship with mRL, plant cover had a negative relationship. rarely develops (Eldridge et al., 2010), but under plants such as Euzomodendron bourgaeanum, Helianthemum almeriense or Acknowledgements. Funding: This study was started in the Salsola genistoides, which are in the Lepra plots, biocrust context of the research projects PECOS (REN2003- (which favours runoff) is much more frequent than the 20% of 04570/GLO) and PREVEA (CGL2007-63258/BOS), both cases that Kidron (2015) found under the canopy at Nizana funded by the Spanish National Plan for RD&I and by the (Israel). This occurs because the canopies of these species are European ERDF Funds (European Regional Development less dense or more separated from the ground. Fund), and continued during the project SCIN (Soil Crust In- We found a positive relationship of mRL with slope, con- terNational, PRI-PIMBDV-2011-0874, European project of sistent in time and space in Cyano and Squam. This agrees with ERA-NET BIODIVERSA, the Spanish team being funded by Chamizo et al. (2012b), who found, in the same study area, that the Spanish Ministry of Economy and Competitiveness). The the effect of slope might be irrelevant at the microplot scale, but work was finally supported and culminated by the DINCOS is important at the small hillslope scale. However, the effect of project (CGL2016-78075-P, Spanish State Programme for slope was mainly due to the S2 plot. This slope effect is logical Scientific Research) and by the European ERDF Funds (Euro- but its significance is relatively unexpected here due to (i) the pean Regional Development Fund). Consuelo Rubio’s partici- opposite effect of the vegetation in the Lepra plots; and, (ii) the pation was possible thanks to the contract as a doctoral student relatively higher RC of the Cyano biocrust (Alexander and FPU18 / 00035. Dr. Javier Barbero advised us on mathemati- Calvo, 1990; Chamizo et al., 2012a) having plots of lower cal issues. steepness. Cerdá and García-Fayos (1997) found a positive Special thanks: This research was kindly facilitated by the relationship between slope and runoff initiation and sediment Viciana brothers, landowners of the El Cautivo field site. yield, but not between slope and runoff volume. The effect of the catchment area was significant, despite the REFERENCES effective contributing area in most plots usually being much smaller than the topographic one. 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Physical basis of the length- Zhang, H., Wei J., Yang, Q., Baartman, J.E.M., Gai, L., Yang, slope factor in the universal soil loss equation. Soil Sci. Soc. X., Li, S.Q., Yu, J., Ritsema, C.J., Geissen, V., 2017. An Am. J., 50, 5, 1294–1298. improved method for calculating slope length (λ) and the LS Mora, J.L., Lázaro, R., 2014. Seasonal changes in bulk density parameters of the Revised Universal Soil Loss Equation for under semiarid patchy vegetation: the soil beats. Geoderma, large watersheds. Geoderma, 308, 36–45. 235–236, 30–38. Puigdefábregas, J., Solé, A., Gutierrez, L., del Barrio, G., Boer, Received 16 June 2021 M., 1999. Scales and processes of water and sediment redis- Accepted 13 September 2021 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Hydrology and Hydromechanics de Gruyter

Defining minimum runoff length allows for discriminating biocrusts and rainfall events

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J. Hydrol. Hydromech., 69, 2021, 4, 387–399 ©2021. This is an open access article distributed DOI: 10.2478/johh-2021-0029 under the Creative Commons Attribution ISSN 1338-4333 NonCommercial-NoDerivatives 4.0 License Defining minimum runoff length allows for discriminating biocrusts and rainfall events 1* 2 3 1 4,5 Roberto Lázaro , Adolfo Calvo-Cases , Eva Arnau-Rosalén , Consuelo Rubio , David Fuentes , 1, 6 Clément López-Canfín Estación Experimental de Zonas Áridas (CSIC), Carretera Sacramento s/n, 04120 La Cañada, Almería, Spain. Inter-University Institute for Local Development (IIDL), Department of Geography, University of Valencia, Edifici d'Instituts, 4ª Planta C/ Serpis 29, 46022, València, Spain. Department of Natural Sciences, Manchester Metropolitan University, John Dalton Building E410a, Chester Street, Manchester M1 5GD, UK. Department of Ecology, University of Alicante, C/ de San Vicente del Raspeig, s/n, 03690 San Vicente del Raspeig, Alicante, Spain. Ecodrone Works, C/ Señores Maripino Rosello, 4, 03550, Sant Joan d’Alacant, Spain. Departamento de Física Aplicada, Universidad de Granada, Avenida Fuente Nueva s/n, 18071 Granada, Spain. Corresponding author. E-mail: lazaro@eeza.csic.es Abstract: The runoff coefficient (RC) is widely used despite requiring to know the effective contributing area, which cannot be known a priori. In a previous work, we defined runoff length (RL), which is difficult to measure. This work aimed to define the minimum RL (mRL), a quantitative and easy proxy of RL, for use in a pilot study on biocrusts in the Tabernas Desert, Spain. We show that RC decreases according to a hyperbola when the contributing area increases, the independent variable being the length of the effective contributing area and its coefficient involving the effects of rainfall and surface features and antecedent conditions. We defined the mRL as the length of the effective contributing area making RC = 1, which is calculated regardless of the area. We studied mRL from three biocrust types and 1411 events clustered in seven categories. The mRL increased with rain volume and intensity, catchment area and slope, whereas plant cover and biocrust succession (with one exception) had a negative effect. Depending on the plot, mRL reached up 3.3–4.0 m on cyanobacterial biocrust, 2.2–7.5 m on the most widespread lichens, and 1.0–1.5 m on late-successional lichens. We discuss the relationships of mRL with other runoff-related parameters. Keywords: Semiarid; Biological soil crust; Runoff connectivity; Length slope factor; Infiltration; Tabernas Desert. INTRODUCTION Non-concentrated runoff seems to form a continuous water sheet on the soil surface during rainfall, whereas infiltration Abundant evidence shows that runoff is highly dependent on occurs simultaneously in a spatially irregular manner dependent rainfall features (volume and intensity), surface hydrological on the distribution of soil features. However, although the water properties (vegetation, biocrust, litter, stones, and other soil sheet completely occupies a surface, runoff does not travel an surface components), soil characteristics (texture, porosity, and undefined length because there is evidence that RC considera- organic matter), previous soil conditions (antecedent soil bly decreases while the considered area increases (Kidron, moisture), and topography (slope angle and contributing area). 2011; Mayor et al., 2011; Xu et al., 2009). The farther a water To study and compare the effects of these multiple factors input occurs from a runoff collector, the lower the amount of controlling runoff, the runoff coefficient (RC) is a widely used that input is collected. According to Lázaro et al. (2015), runoff parameter. length (RL) is the length of the hillslope travelled by runoff; Nevertheless, using the RC, requires knowing the that is, for any point, RL is the maximum distance, in a straight line following the maximum slope line, from which the runoff contributing area. Closed runoff plots (surrounded by a wall delimiting the monitored drainage area) have been widely used comes. (RL is different from the length of the path travelled by under the assumption that the complete delimited area is the water, which depends on the surface microtopography). RL is effective drainage area. Because this assumption is unfounded important because it (i) contains some information on the hy- (Kidron and Yair, 1997; Kidron, 2011), delimiting an area does drological connectivity, because at least the drainage area de- not make sense and, open runoff plots are preferable because limited by RL is necessarily fully connected; (ii) enables effi- they do not alter the natural fluxes and prevent the relative cient comparisons of the hydrological properties of different exhaustion of sediments (Boix-Fayos et al., 2006). However, surface types, rainfall types, and minimum inter-event times using open runoff plots, we continue without knowing the (MITs), etc., at least because it allows for determining the effective contributing area, even if we topographically delimit drainage area by its length; (iii) provides information on the an area in situ, which would be the maximum possible sediment transport capacity; and (iv) seems to have potential to contributing area. Thus, we should assume that we never know enable predictions about runoff flow at a point as a function of a priori the real drainage area corresponding to a runoff rainfall. measurement nor, consequently, the real RC. Therefore, we However, because RL cannot be directly observed, the RL need an alternative parameter enabling characterisation of the concept is elusive. Little is known about the RL values in given hydrological behaviour. circumstances, although Agassi and Ben-Hur (1991) studied the 387 Roberto Lázaro, Adolfo Calvo-Cases, Eva Arnau-Rosalén, Consuelo Rubio, David Fuentes, Clément López-Canfín effect of slope length on infiltration and runoff. Puigdefábregas spiration is around 1600 mm, water deficit occurs every month, et al. (1999) and Arnau-Rosalén et al. (2008) suggested that the in particular during summer (June–September). Insolation is slope length travelled by runoff is often only a part of the over 3000 hours per year, and the average annual temperature is catchment length. This idea also underlies the work of 18 °C (Lázaro et al., 2004). The study area was the El Cautivo Puigdefábregas (2005), who stated that temporal variability of field site, within the Tabernas Desert. Although calcareous rainfall controls runoff re-infiltration and its decay with slope sandstones are locally abundant, Miocene soft marine marls length. Lázaro et al. (2015) experimentally determined RL on dominate the lithology and produce an extensive badlands biocrusts, although at only 1 m of spatial resolution. However, landscape and a complex geomorphology developed during the such experiments were logistically complex and time consum- Quaternary (Alexander et al., 1994; Alexander et al., 2008). ing. Here, we propose a high-resolution, quantitative subrogate The parent material is mainly composed of silt-size (>60%), of RL that is simple and easy to measure, using data from the gypsum-calcareous and siliceous particles; fine sand ranges same study area. from 20% to 35%, and clay ranges from 5% to 10%. (Cantón et Biocrusts are complex communities constituted by microor- al., 2003). El Cautivo includes a series of parallel catchments, ganisms, lichens, bryophytes, fungi, and algae inhabiting the with residual hanging pediments between some of them. A soil surface and within the upper soil centimetres. They are clear surface-type pattern exists. A third of the territory is bare widespread on a planetary scale (Büdel, 2003) at the sites and eroded; biocrust is the main cover in another third; and also where vascular plants are limited by climatic factors, and they occupies the plant interspaces in the rest (Cantón et al., 2004; play an important ecological role because they affect almost Lázaro et al., 2000; Lázaro et al., 2008). every ecological process (Belnap and Lange, 2003; Maestre et The biocrust types described by Lázaro et al. (2008) in this al., 2011; Webber et al., 2016). Chamizo et al. (2016) published study area were simplified to three for this research: (i) domi- a review on the biocrusts’ hydrological role. Biocrusts consti- nated by Cyanobacteria (Cyano); (ii) dominated by the lichens tute a good system model (Bowker et al., 2010; Maestre et al., Squamarina lentigera and/or Diploschistes diacapsis (Squam); 2016) as well as adequate surface cover to study runoff due to and (iii) characterized by the lichen Lepraria isidiata (Lepra). the existence of previous experimental studies in the same area The site of Cyano where the runoff plots were constructed has a (e.g., Chamizo et al., 2012a; Lázaro and Mora, 2014; Solé- mature, relatively rough cyanobacterial biocrust, including Benet et al., 1997). On the other hand, biocrusts develop in small pioneer lichens, such as Endocarpon pusillum, Fulgensia plant interspaces where vegetation cannot form a continuous desertorum, and Fulgensia poelti. This biocrust is the colo- layer (mostly in drylands), and they are considered runoff nizing one (beginning with a purely cyanobacterial biocrust) sources, providing water to the plant patches (Rodríguez- and is widespread in any orientation, constituting a matrix-like Caballero et al., 2014; 2018). Thus, knowing their RL would layer on which the other biocrust types successively develop provide insights to advance the current source–sink theory. when possible. In the sunniest non-eroded sites, Cyano is dom- The initial hypotheses were as follows: inant and almost permanent. Squam is the most widespread a) RL is often much shorter than the topographical lichen-dominated biocrust. It usually develops after Cyano, drainage area, which represents the historical maximum of RL. preferring the unaltered north-to-east hillslopes with low plant Kidron and Yair (1997), Puigdefábregas et al. (1999), and cover, and including numerous lichen species, such as Buellia Puigdefábregas (2005) and Arnau-Rosalén et al. (2008) already zoharyi, Fulgensia fulgida, Diploschistes ocellatus, and Psora made suggestions in this line. decipiens. Lepra biocrust is late successional and exclusive to b) RL widely varies across numerous factors, such as the the shadiest north-faced hillslopes, where it occupies the plant rainfall features (intensity, volume and timing), the surface interspaces. Lichen species such as Squamarina carthilaginea, characteristics (including vegetation, soil, topography, Xantoparmelia pokornyi, and Teloschistes lacunosus are char- biocrusts, and stoniness), and the antecedent soil moisture. acteristic of Lepra, as well as some mosses such as Grimmia Because runoff strongly depends on these factors (Castillo et pulvinata, Didymodon luridus, and Tortula revolvens. al., 2003; Le Bissonnais et al., 1995), we assume that RL will also depend on them. Runoff monitoring c) In the study area, RL will be centimetres long rather than metres long for most natural rainfall (Lázaro et al., 2015), Two open runoff plots and a rain gauge were installed in which very often has low intensity or small volume (Lázaro et each biocrust. The plots at Cyano were labelled C1 and C2, al., 2001). those of Squam S1 and S2, and those at Lepra L1 and L2. Their d) Biocrust will generally have high RC, but it will vary appearance is shown in Fig. 1. The available data cover approx- according to its species composition (Lázaro et al., 2015). imately 10 years (2005–2015). Each plot consists of a PVC The objectives of this work were (i) to define the minimum channel, normal to the line of maximum slope, collecting runoff RL (mRL) and propose it as a concrete, quantitative, and easy and driving the water to a tank at the bottom of the hillslope. proxy of RL, and (ii) to use mRL for a pilot study to show the The channels, covered with a lid to avoid direct rain, are em- effect of biocrust type and rainfall class on RL from open run- bedded into the soil, and the contact of its upslope edge with off plots. the soil was in situ plasticised by means of fiberglass and epoxy resin, warranting the transit of the runoff to the trough. Inside METHODS the tank is a non-purpose tipping-bucket mechanism (0.5 L in The study area and the runoff plots resolution) connected to an on–off Hobo Event data logger, like that of the rain-gauge (0.25 mm in resolution). The Tabernas Desert is a place in southeast Spain, in the Sorbas–Tabernas basin, surrounded by the Gador, Nevada, Definition and calculation of mRL Filabres, and Alhamilla Betic ranges. The first three of these ranges intercept most rainfall fronts, which come mainly from Because the effective contributing area is not known the west, explaining the annual precipitation of around 230 mm a priori, examining the way RC varies in relation to it becomes (Lázaro et al., 2001). Because the annual potential evapotran- essential. To conduct this theoretical examination, we used 388 Defining minimum runoff length allows for discriminating biocrusts and rainfall events three minimum inter-event times (MITs): 24, 12, and 1 hour, values that are larger than 1 simply mean that runoff comes constructing three datasets with 436, 593, and 1411 rainfall – from upslope of the length attributed to the drainage area. The runoff events, respectively. For every event and each plot, we larger than 1 the RC value is, the larger the mRL is in relation calculated four RC values by successively assuming different to the supposed length. As can be verified from Equation (1), lengths (1, 2, 3, and 4 m) for the effective contributing area. when RC = 1, x = a. Therefore, we can define the following: These hillslope lengths, multiplied by the width of the plot mRL = a = R / P × cw (4) (m) (L) (mm) (m) (length of the collector, 2.18 m except for L2, at 2.16 m) gave rise to four nested, rectangular, and progressively larger sup- Note that in Equation (4), only three known parameters in- posed drainage areas per event, generating four RC figures. tervene, and the contributing area does not. This procedure implies assuming that they were ideal smooth To show these hyperbolic relationships, we used Equation and homogeneous hillslopes. Our real plots only approximate (1) to plot the hyperbolas of the average (thus blurring the these conditions, but this preliminary assumption is useful to effect of the antecedent soil moisture) RC vs lengths succes- explain the concept and calculation of mRL. Next, we applied sively assumed for the contributing area, for one plot of each this approach to real data, examining the way RC varies when biocrust type and two different rainfall classes. Later, to explore successively larger portions of the real catchment are consid- the effect of rainfall type on runoff, we classified the rainfall ered effective contributing areas. events into seven categories: >0–1, >1–3, >3–5, >5–10, >10– As the width of the plot is assumed to remain constant for 20, >20–30, and >30 mm. Because most of the rainfall events any channel length, the assumption of a series of hillslope were small, we divided the group of events ≤5 mm into three lengths (for the supposed effective drainage area) increasing classes to avoid an extremely large lower class and to gain according to the series of natural numbers produces a series of resolution to establish the rainfall threshold generating runoff. nested areas, increasing in arithmetic progression. Because runoff must be divided by the area, while the plot length in- Analysis of mRL at El Cautivo field site throughout creases linearly, the corresponding RC potentially decreases because the value of a series of fractions with arithmetically biocrust types and rainfall events increasing denominators decreases according to a potential curve of exponent –1, forming a hyperbola. Thus, for any pair On natural hillslopes whose topography generates somewhat of runoff and precipitation values (i.e., for any rainfall or sur- irregular drainage areas, in such a way that a regular increment face type and any slope angle), the RCs generated by assuming in the length of the supposed effective catchment does not successively longer contributing areas always decrease accord- imply a regular increment in its area, the theoretical relationship in Equation (1) is only fulfilled in an approximate way and a ing to the following curve: potential curve must be fitted. –1 RC = a × x (1) To examine the variation of RC with the length of the sup- posed contributing area using real data from El Cautivo runoff where x is the length of the part of the hillslope that is assumed plots, we first determined the perimeter of the catchment of each to be the effective contributing area and a is a coefficient that plot. Then we calculated the successively larger real areas de- varies widely, because it involves the effects on runoff of the limited by successive 10-cm buffers in parallel to the trough. rainfall and surface characteristics, and can be experimentally To establish the catchment areas and soil surface compo- calculated. nents, a series of manual photogrammetric flights were carried Thus, although we cannot calculate RC, we can determine its out by means of a DJI Phantom 4 Pro drone carrying a high- distribution. Furthermore, for a rectangular plot, RC is as fol- resolution, 1-inch sensor (20 Mp). Images were taken at 3.5–5 lows: m above ground level, combining nadir and oblique images with an estimated overlap of 80 and 70% (forward and side, RC = R(L) / (P(mm) × cw(m) × x(m)) (2) respectively) to obtain an average of 596 images per experi- mental plot. Images were processed in Agisoft Metashape Pro where R is the runoff measured in litres, P is the measured (L) (mm) (Agisoft LLC, Russia). Resolution ranged from 0.95 to 1.13 precipitation in millimetres, cw(m) is the width of the collector –1 –1 mm pixel and 1.9 and 2.7 mm pixel for orthomosaics and the in metres, and x(m) is the hillslope length of the supposed effec- digital elevation model, respectively. tively contributing area in metres. Therefore, it is After removing most of the plants, using the Agisoft Metashape image classification software and then manually, the a = R(L) / P(mm) × cw(m) (3) digital terrain model was processed to identify the catchment areas draining to the collectors (Hydrology Tools, ArcMap 10.8). These curves relating RC with the length of the contributing Then, each catchment area was divided into parallel 10-cm area for any event of any surface type are determined by only bands, parallel to the runoff collector (Multi-ring Buffer, QGIS one parameter (a). Any value for length leads to a value for RC 3.14). From the digital terrain model, the average slope of each that exactly matches a point in the hyperbola. Because the catchment was also obtained (Zonal Statistics, ArcGis 10.8). hyperbola has an indefinite length, a length of contributing area Thus, every regular increase in slope length corresponds to a corresponding to RC = 1 always exists, independently from the different, but real, increase of contributing area. Then we calcu- surface and rain characteristics. As some infiltration always lated the RCs for every area (10 cm longer than the previous), occurs, the actual RL will be larger than the hillslope length plotted those RCs vs the hillslope length, and fitted a potential corresponding to RC = 1 is. Therefore, the hillslope length of curve. In a first step, we did this not for any concrete event but the supposed effectively contributing area corresponding to RC = 1 can be considered the minimum RL (mRL) for the for the average and for the maximum RCs of every rain type given set of circumstances (rainfall event, surface and anteced- and every biocrust type to verify the quality of the fittings and ent conditions) and enables an easy definition for mRL. This obtain a graphical reference of the mRL values. means that the minimum hillslope length travelled by runoff for We determined the cover of vascular plants, biocrusts, and a certain site and event is larger than the mRL. RC hyperbola bare soil in each plot by adding the segments occupied by every 389 Roberto Lázaro, Adolfo Calvo-Cases, Eva Arnau-Rosalén, Consuelo Rubio, David Fuentes, Clément López-Canfín C1 C2 S2 S1 L1 L2 Fig. 1. El Cautivo hillslope scale open runoff plots. surface type at 1 mm resolution in transects along the catch- and the covers of vascular plants in the catchment areas delim- ment area drawn on the plot orthophotomap (to avoid trampling ited by 1 m, 2 m, and 8 m upstream of the channel were also the plots). The length occupied by each type of coverage in initially considered as covariates. Instantaneous rain intensity relation to the total length of the transect was directly consid- was calculated for every rainfall record (rainfall volume input ered its cover percentage. divided by the difference between the time of that record and We used Equation (4) to calculate mRL directly for every the time of the previous), and the data used here were the aver- rain and runoff event of each MIT (24, 12 and 1 hour). We age and the maximum intensities for each event. Then, we carried out generalized linear modelling analyses to test for reduced the number of covariates, taking into account their differences in mRL according to two factors and their interac- interrelationships, the available statistical power, and the signif- tion: rain classes (seven categories) and biocrust types (three). icance levels that the covariates reached in preliminary, tenta- We explored the instantaneous rain intensity and the rain dura- tive analyses (see in Results). To perform these analyses, we tion as covariates; the volume of precipitation was not included selected a gamma data distribution and log as link function, due to its redundancy with the rain class factor. To account for including the records having mRL larger than zero, and used the differences among individual plots, catchment areas, slope Statistica 7.1 software (StatSoft, Hamburg, Germany). angles, the covers of vascular plants, biocrusts, and bare soil, 390 Defining minimum runoff length allows for discriminating biocrusts and rainfall events RESULTS Every pair of plots on the same kind of surface have a simi- Features of runoff plots and rainfall events lar hydrological behaviour (Fig. 2), except for Squam biocrust. The shape of the point clouds in Fig. 2, resembling a partially The characteristics of the runoff plots determined by analys- open “fan” and curved upwards, shows the increasing effect of ing the drone images are shown in Table 1. rain intensity and antecedent soil moisture as the precipitation The duration, volume, intensity, and number of events for volume increases. The amplitude of these “fans” shows the every rain type and every MIT are summarized in Table 2. variance due to the rainfall type and timing. Additionally, we The regression coefficient between runoff and rainfall was can obtain an idea about the effect of biocrust type on runoff by quite similar for the events from the three MITs in every plot comparing the scaling in the y-axes. and slightly higher for the 1-hour MIT (0.630 on average vs Rainfall volume to start runoff progressively increases 0.572 and 0.575 for the 24- and 12-hour MITs, respectively). through biocrust types; it is short at Cyano, medium at Squam, Thus, we show the analyses with the 1-hour MIT, which, and larger at Lepra. Considering all the plots and events of the moreover, produces the largest number of events. The larger 1-hour MIT, we found 2336 cases (sum of events including all maximum rain intensity belonged to event class 5 (although the the plots) with an mRL equal to zero and 21 with an mRL larg- average intensities were not very different among MITs). er than zero within the rainfall class 1. The same values were, The very large maximum intensity recorded in event class 1 respectively, 1029 and 70 for class 2; 305 and 121 for class 3; when we used MIT 1 lasted 5 seconds and did not generate 181 and 245 for class 4; 85 and 215 for class 5; 9 and 81 for runoff. class 6; and 3 and 33 for class 7. Table 1. Features of the runoff plots used at the El Cautivo field site. Biocrust types are described in the main text. Area is the contributing area according topography (m ). Length is the slope length of the area (m). Slope is the average slope angle (degrees). Aspect is the general orientation (degrees in eastward direction). Covers are given as %. Plant cover 1 m is the plant cover in the first meter upstream from the collector. Aspect Plant Biocrust Bare Plant Plot Biocrust Area Length Slope eastward cover cover cover cover 1m C1 Cyano 8.59 7.04 24.46 265 22.13 73.65 4.22 8.45 C2 Cyano 10.79 6.19 16.79 84 8.58 81.63 9.79 5.87 S1 Squam 19.15 13.64 33.18 7 27.04 70.20 2.76 14.24 S2 Squam 22.38 9.72 43.59 4 11.58 69.00 19.42 27.30 L1 Lepra 21.91 12.56 40.92 20 30.95 57.94 11.12 5.59 L2 Lepra 31.08 11.44 41.96 22 34.57 54.05 11.37 49.10 Table 2. Features of the rainfall events; averages from the three rain-gauges. Average and maximum duration are in days; average volume is rainfall in mm; average and maximum intensity are in mm/hour. *Remember that maximum intensity lasted only 5 seconds. 1 2 3 4 5 6 7 Rain class >0–1 mm >1–3 mm >3–5 mm >5–10 mm >10–20 mm >20–30 mm >30 mm number of events 199 72 31 42 52 21 19 average duration, days 0.33 0.65 0.80 1.18 1.33 1.73 2.68 maximum duration, days 3.26 4.16 3.25 8.93 4.60 4.66 6.86 MIT 24 h average volume, mm 0.32 1.72 3.63 6.58 13.13 23.31 39.07 average intensity, mm/h 5.75 0.64 0.40 0.85 0.96 1.22 1.21 maximum intensity, mm/h 542.99* 12.08 1.15 13.17 8.48 7.06 7.13 number of events 323 94 36 48 54 22 16 average duration, days 0.14 0.29 0.50 0.56 0.80 1.17 1.26 maximum duration, days 0.86 0.90 1.94 2.02 2.96 3.62 2.61 MIT 12 h average volume, mm 0.27 1.66 3.74 6.53 12.93 24.69 34.83 average intensity, mm/h 1.37 1.06 0.48 1.03 1.23 1.56 1.74 maximum intensity, mm/h 20.27 12.08 1.26 13.17 8.48 7.06 7.13 number of events 1014 184 71 71 50 15 6 average duration, days 0.02 0.06 0.10 0.16 0.25 0.30 0.39 maximum duration, days 0.12 0.27 0.34 0.41 0.76 0.74 0.68 MIT 1 h average volume, mm 0.22 1.64 3.62 6.76 13.38 23.55 36.16 average intensity, mm/h 1.57 2.33 2.73 3.07 3.67 5.51 4.61 maximum intensity, mm/h 20.27 18.41 19.44 18.61 40.88 20.12 9.16 391 Roberto Lázaro, Adolfo Calvo-Cases, Eva Arnau-Rosalén, Consuelo Rubio, David Fuentes, Clément López-Canfín Fig. 2. Runoff (y-axis in litres) vs rainfall (x-axis, mm). Data are the total of each event, using the 1411 events distinguished by the 1-hour MIT. Every graph shows the two plots of the same biocrust type. Graphs A, B, and C correspond to Cyano, Squam, and Lepra, respectively, and are presented in ascending successional order. Note that the scales of the y-axes are different. Fig. 3. Examples of hyperbolas relating to the RC with the length of the supposed effective contributing area. For each plot, we use the mean runoff and precipitation of all events of the rainfall classes 3 (>3–5 mm) and 5 (>10–20 mm), generated with the 1-hour MIT. For every pair of rain and runoff data points, we successively assumed four rectangular, nested, effective contributing areas having the length of the channel as width and 1, 2, 3, and 4 m as length. All hyperbolas are asymptotic with respect to the Y axis, thus, a length for the effective contributing area that makes RC = 1 always exists. A RC value > 1 or >> 1 indicates that the assumed length for the contributing area is less or much less than the real one. Theoretical curves of decrease of RC according to regular based in the maximum runoff peaks, the average runoff, or any increase of contributing area other runoff parameter. The maximum mRL (Fig. 4) was be- tween 3.3 and 4 m at Cyano, about 2.2 m at S1 (although it was The RC hyperbolas differed in the distance of the vertex about 7.5 m at S2), and between 1.0 and 1.5 m at Lepra. from the origin of coordinates, which vary according to surface Using the 12-hour MIT and 24-hour MIT, the number of types, topography, antecedent soil moisture, rainfall types, etc. events changes, as well as the proportion of events belonging to Fig. 3 shows some examples for theoretical regularly increasing every rainfall class. However, the goodness of fit and the gen- areas. Even for a surface with high infiltration (with the hyper- eral features of the results are practically the same as those bola vertex close to the coordinates’ origin), a positive slope shown in Fig. 4. length for which RC = 1 (an mRL value) always exists. Fig. 5 shows that runoff peaks were different in every bi- In these theoretical curves, the greater the MIT, the greater ocrust, as well as for every rain class. Note that the largest RCs the RCs and the further the hyperbola vertex were from the are produced by rain class 5. origin of the coordinates, because of the greater proportion of These graphs offer an understanding of the relationship be- large events (Table 2). tween RC and contributing area, verify the goodness of the fit, and provide a graphical value of mRL. Once a good fit was Goodness of fit of the real drainage areas to the theoretical established, we analysed mRL data calculated event by event hyperbolas by using Equation (4). When we used successive bands of the real catchment areas Analysis of mRL with regard to rainfall, surface and of every plot to exam the relationship between RC and increas- topography features ing contributing areas, the fit of the hyperbolas (Fig. 4) was very good, because the plots’ catchments are vaguely smooth The analyses showed significant differences in mRL accord- and rectangular, at least along the hillslope meters closer to the ing to all of the factors and included covariates. Rain duration and the cover of bare soil were removed because they were not channel. significant when analysed along with the other variables. The The abscissa corresponding to the point where the hyperbola biocrust cover was also removed because it shows a clear nega- crosses the value 1 of ordinates is the mRL. These curves show tive relationship (R = 0.86) with plant cover. The plant cover that for any surface and rainfall, maximum RCs are much larger within 1, 2 and 8 m upstream from the runoff collector, alt- than average. Therefore, for a case in which a curve refers to a hough often independent from the general plant cover, were set of events, it is crucial to specify whether the used mRL is 392 Defining minimum runoff length allows for discriminating biocrusts and rainfall events Fig. 4. Difference between the average and maximum runoff. Hyperbolas fitting the variation of RC when successively larger portions of the real topographic catchment of every plot, delimited by parallel lines spaced 10 cm from each other, are assumed to be the effective contributing areas. Data using the 1-hour MIT. All hyperbolas are asymptotic with respect to the Y axis, thus, a length for the effective contributing area that makes RC = 1 always exists. A RC value > 1 or >> 1 indicates that the assumed length for the contributing area is less or much less than the real one. Fig. 5. Graph A: Hyperbolas of RC vs contributing area for each plot using the maximum RC of the entire event series and the bands of the real topographical catchments. Graph B: Hyperbolas using the maximum RC of the event classes in the most responsive runoff plot (S2), and the bands of the real topographical catchments (R are the same for all the rain classes because all the curves refer to the same plot and to the same increments of contributing area). Both graphs used data from the 1-hour MIT. All hyperbolas are asymptotic with respect to the Y axis, thus, a length for the effective contributing area that makes RC = 1 always exists. A RC value > 1 or >> 1 indicates that the as- sumed length for the contributing area is less or much less than the real one. 393 Roberto Lázaro, Adolfo Calvo-Cases, Eva Arnau-Rosalén, Consuelo Rubio, David Fuentes, Clément López-Canfín also removed to gain statistical power and used in alternative An mRL threshold in at about 3 mm of rainfall has been found analyses instead of the general plant cover. Thus, the final (Fig. 6): At less than 3 mm of rainfall, the peaks of mRL never analysis included both factors (biocrust type and rain class) and reached 10 cm (runoff was rare in rain classes 1 and 2, but their interaction, three covariates to account for the features of sometimes it occurred; see above). every particular plot (catchment area, slope, and plant cover), The biocrust type significantly affected the mRL (Fig. 7A), and the rain intensity as an additional covariate, because it is and when we removed the data from plot S2, the mRL decreased poorly related to the rainfall volume. Table 3 summarizes the along biocrust succession (Fig. 7B). However, the features of results of the final analysis. S2, with much larger runoff due to other factors (such as larger The mRL consistently increases when rainfall increases, and bare soil area and slope angle), deform the relationship between the differences between rain classes are often significant. mRL and the successional sequence if S2 is included. Table 3. Significance of the effects of the different factors, interactions, and covariates on mRL, according to hypothesis testing using generalized linear modelling. Effect Degrees of Log- Chi- p freedom likelihood square Event class 6 –205.644 221.2202 0.000000 Biocrust type 2 –164.662 81.9652 0.000000 Event class × Biocrust type 12 –146.243 36.8361 0.000237 Rain intensity 1 –476.893 56.0725 0.000000 Catchment area 1 –464.168 25.4504 0.000000 Slope angle 1 –456.728 14.8815 0.000114 Plant cover 1 –316.254 280.9465 0.000000 bc Fig. 6. Average mRL for the sets of events in every rain class produced using an MIT of 1 hour, including the data from all the plots. Different letters on the boxes indicate significant differences. 1.8 0.8 1.6 0.7 a 1.4 0.6 1.2 0.5 1.0 0.4 mRL 0.8 0.3 0.6 0.2 0.4 0.1 0.2 Mean Mean±SE Mean±0.95 Conf. Interval Mean Mean±SE Mean±0.95 Conf. Interval 0.0 0.0 Cyano Squam Lepra Cyano Squam Lepra Biocrust type Biocrust type Fig. 7. Differences in mRL according to biocrust type. Graph A includes all the plots, and the differences are highly influenced by the larger runoff in plot S2. Graph B does not include the data from plot S2 and shows that infiltration increases along the ecological succes- sion. Different letters on the boxes indicate significant differences. mRL mRL Defining minimum runoff length allows for discriminating biocrusts and rainfall events S1 S2 mRL Mean; Whisker: Mean±SE -1 12 345 67 Event Class Fig. 8. Interaction between biocrust type and rain event class. Every line corresponds to a biocrust type, but for Squam the plots are shown separately because they behave quite differently. Except for plot S2, mRL decreases along biocrust succession. The threshold of mRL at 3 mm rainfall is distinguishable in this figure as well. The interaction between biocrust type and rain class is before reaching the collector. This threshold plot length is RL, a shown in Fig. 8. The larger the rainfall, the larger the difference concept providing a measurement of the decay of RC as the in mRL is among biocrusts. Biocrust type modulates the way in drainage area increases. Connectivity is usually larger, some- which the different rainfall classes affect runoff. However, the times drastically larger, than RL. difference is also due to the slope and other causes such as plant To explore and discuss the relationship of RL or mRL with and bare soil covers; the influence of plot S2 expanded the the length slope factor (LSF) or potential sediment transport range of mRL along the event classes in the Squam biocrust. index (Moore and Burch, 1986), a parameter derived from the Average rain intensity, contributing area and slope angle had digital elevation model, could be interesting. The LSF is a a positive significant effect on mRL, whereas plant cover had a surrogate that indicates the erosive potential of runoff, and its negative significant effect (Table 3). When we carried out the formula is LSF = (Xh / 72.6) , where Xh is the horizontal alternative analyses replacing plant cover successively by the length in meters of the slope and m is the exponent of the slope plant cover at 1, 2, or 8 m upstream of the channels, each cover variable, defined as m = ɛ / (1 + ɛ). The term ɛ relates to erosion showed a significant effect on mRL. in the furrows and between furrows and is defined as ɛ = 0.8 The number of events decreases when the MIT increases sin / 0.0896 × (3 × (sin ) + 0.56), where is the angle of and, whereas the duration of the events tends to increase expo- the slope (McCool et al., 1997; Zhang et al., 2017). RL and nentially when MIT increases, the rain intensity tends to de- mRL should relate closely to LSF because the (potential) crease potentially when MIT increases. However, the general- transport capacity of sediments depends on runoff. Interesting- ized-linear-model results show the same pattern with all the ly, LSF is a factor deduced from topography, but mRL is calcu- MITs, with all the considered factors, interactions, and covari- lated from runoff and precipitation from specific events. In ates of the final model being significant. reality, both concepts are independent and complementary approximations. As a first tentative hypothesis, if we replace DISCUSSION the slope length with the mRL in the LSF formula, the resulting RL and mRL potential sediment transport capacity would become actual capacity, that is, actual sediment transport if sediments are RL and mRL are different from hydrological connectivity. A available. This could be verified empirically, and if so, mRL stream or river can connect large distances; however, a certain could be highly useful for a predictive erosion model where concrete water volume usually does not cover all the connected sediment availability is not a limiting factor. distance because it stops at some point on the shore, infiltrates, As Lázaro et al (2015) discussed, the “flow length index” of evaporates, or is absorbed by plants. Similarly, when diffuse Mayor et al. (2008) is conceptually comparable to RL. Howev- surface runoff (not concentrated in rills) occurs, the entire er, it does not include the incoming rainfall. hillslope length can be hydrologically connected, but that does The slightly higher regression coefficient between runoff not necessarily mean that RL is the entire hillslope length. and rainfall for the 1-hour MIT we found agrees with the results (However, it is certain that all the space covered by RL is con- of Molina-Sanchís et al. (2016). nected.) If we progressively increase the length of the plot We believe that mRL is a proxy of RL with general validity. undergoing simulated rainfall, runoff volume increases until a By changing the rainfall or surface features, the parameter ‘a’of certain plot length (Lázaro et al., 2015) because, beyond that Equation (1) changes, but it does not change the concepts or length, all the water felt in the upper end of the plot infiltrates interpretations of the processes. The hyperbolic relationship we mRL Roberto Lázaro, Adolfo Calvo-Cases, Eva Arnau-Rosalén, Consuelo Rubio, David Fuentes, Clément López-Canfín found between RC and real drainage area length (Fig. 4) is 2007). Our result partly agreed with Belnap (2006), who found consistent with the potential decrease of RC experimentally two hydrological behaviours: Green algae and microfungi be- determined by Lázaro et al (2015). In the experiments, the have similarly to cyanobacteria, whereas bryophytes are similar curves fit worse because different plots (although close, homo- to lichens. geneous, and under the same simulated rainfall) represented the Because the development of some biocrust types takes long- different lengths. The goodness of the fits in Fig. 4, along with er than that of others, and eventually one type is replaced by a certain irregularity of the shapes and micro-reliefs of our real another (Lázaro et al., 2008), it is widely agreed that different drainage areas, show that our proposal is applicable in an ex- biocrust types can be understood as successional steps (Belnap tensive range of plots, because when we installed our plots in et al., 2006; Li et al., 2013; Rodríguez-Caballero et al., 2015), 2005, we did not look for ‘ideal-like’ hillslopes. although some scholars do not regard different crust types as being necessarily successional stages (Kidron, 2019). In our Runoff on biocrusts at the El Cautivo field site area, the succession begins from Cyano and progresses to Squam and finally to Lepra (Lázaro et al., 2008). However, As expected, the larger the rainfall, the larger the mRL. We succession shows different speeds at different habitats and can found occasional runoff even in rain classes 1 and 2, which stop at any point. It strongly depends on the microclimate, Rodríguez-Caballero et al. (2014) also found in the same study mainly on sun radiation and water availability. Where there are area. Despite an mRL value existing as long as the runoff is not conditions for development of lichens or mosses, Cyano can measurable, a clear threshold can be observed in the relation- be almost permanent on a human life timescale. ship between mRL and rainfall (Fig. 6). The way in which the Except for plot S2, our results show that infiltration tends to rain class affected the mRL depended often on the biocrust type increase along biocrust succession. This is consistent with our (Fig. 8). Lázaro et al. (2015) also observed that interaction: A previous experiments and with Gypser et al. (2016). Although threshold of runoff vs rainfall is associated with a different rain biocrusts are often considered runoff sources (Cantón et al., class depending on the biocrust type. 2002; Rodríguez-Caballero et al., 2018), their RC is generally The larger the rain intensity, the larger the mRL. This caused lower than that of bare soil with physical crust (Eldridge et al., that the rain class 5 gave rise to the largest runoff coefficients 2020) because biocrust succession progressively increases (Fig. 5B), despite classes 6 and 7 involving larger rainfall vol- water retention (Gypser et al., 2016) and soil moisture (Chami- umes, as the intensity of class 5 was clearly larger when using zo et al., 2013). This increase of infiltration along succession is MIT 1 (Table 2). This is consistent with what was previously due to multiple factors, including (i) the effect of pore clogging stated in the same study area, under natural rainfall (Rodríguez- increasing runoff in the early successional stages, favoured by Caballero et al., 2014) and rain simulations (Lázaro et al., cyanobacterial exopolysaccharides (Kidron et al., 1999); (ii) the 2015). The same was found in other locations (Guan and Cao, increase of surface roughness increasing infiltration as the 2019). succession progresses (Chamizo et al., 2010; Kidron, 2007; As expected, there were significant differences in mRL Rodríguez-Caballero et al., 2012); and (iii) the larger proportion among biocrust types. Except for the Squam biocrust, the dif- of mosses and vascular plants in the latest-successional biocrust ferences among plots belonging to the same biocrust type were (Lázaro et al., 2008), because mosses show larger infiltration much smaller than the differences among types (Fig. 2). The capacity than do lichens (Fischer et al., 2014). In addition, larger slope of plot C1 with regard to C2 was compensated by a plants, which develop progressively, are the main runoff sinks lower contributing area. The lower plant cover of plot L1, par- (Minea et al., 2018; Solé-Benet et al., 1997). Hydrological ticularly in the first meter upstream of the collector (Table 1), changes associated with successional stages have also been compensated for its smaller drainage area. However, the two found in more mesic and larger vegetation including biocrusts plots at the Squam biocrust behaved differently. Much larger (Lichner et al., 2012). runoff was consistently recorded for plot S2 during the sampled Comparable data on RL from other areas are scarce. Kidron period. It has larger slope, less plant cover, and much higher (2011) reported an average RL of 5.0 m, while Kidron and Yair cover of bare soil, with its upper part eroded (Table 1). The (1997) estimated a length of 7 to 10 m for the effective contrib- slope angle in S2 is 45º in the first 8 m upstream of the collec- uting area in the case of the peak runoff produced at the end of tor, which is relevant because the maximum recorded mRL was the heaviest storm, when the biocrust was already saturated, in shorter than 8 m. We did not find in the literature a slope their most responsive plot, which had only 10% of plant cover threshold beyond which runoff disproportionately increases. and a relatively smooth biocrust. This length is close ourmaxi- However, where soil is silty, runoff is larger on bare than on mum mRLvalue, which reached 7.5 m in our most responsive biocrusted soil (Wei et al., 2015; Xiao et al., 2019). Soil texture plot. seems determinant: In Tabernas’ silty soils, biocrusts often To our knowledge, this is the first study on the hydrological generate less runoff than bare soil, but in the sandy soils of the behaviour of the Lepra biocrust. Chamizo et al. (2012a; 2012b) Negev, biocrust shows threefold higher runoff than bare soil and Lázaro et al. (2015) did not include Lepra to avoid severe (Kidron, 1999). Chamizo et al. (2012a) and Lázaro et al. (2015) alterations, as its typical large slope angle generates significant also found significant differences in runoff between biocrust challenges in the experiments. This is interesting because Lepra types. Although cyanobacterial biocrusts tend to produce larger is the permanent biocrust community that occupies the plant mRL, Rodríguez-Caballero et al. (2013) and Chamizo et al. interspaces in non-eroded mature grassland or scrubland sites. (2012b) noted that the difference in runoff between cyanobacte- Furthermore, because the sites chosen for the Lepra plots have rial and lichenic biocrusts decreases to nothing as rainfall vol- relatively low grass cover, the runoff will be still lower in ma- ume increases. Our result is consistent with Kidron et al. ture grasslands. (2003), who found in Negev a substantial reduction in the RC The mRL is consistently lower in Lepra over time, despite from cyanobacterial to moss-dominated biocrust, explained by the slope, because of the greater plant cover (Minea et al., the lower amounts of extracellular polymeric substances and 2018) and number of small plant patches and annual plants. the higher roughness of moss-dominated biocrust. Small differ- First, there is a larger number of plant roots acting as preferen- ences in the micro-relief already affect the runoff (Kidron, tial infiltration routes; second, fine-grained plant patches are 396 Defining minimum runoff length allows for discriminating biocrusts and rainfall events more efficient in reducing runoff than the coarse-grained ones intensity), as well as those of the surface (biocrust type and (Bautista et al., 2007). In addition, soil porosity is larger under plant cover) and those of topography (contributing area and plants (Mora and Lázaro, 2014), and plants further increase slope angle), determined mRL. Different biocrusts had different infiltration by intercepting rainfall and producing stemflow mRLs and whereas rainfall, area, and slope had a positive (Jian et al., 2018). Furthermore, under alpha grass, biocrust relationship with mRL, plant cover had a negative relationship. rarely develops (Eldridge et al., 2010), but under plants such as Euzomodendron bourgaeanum, Helianthemum almeriense or Acknowledgements. Funding: This study was started in the Salsola genistoides, which are in the Lepra plots, biocrust context of the research projects PECOS (REN2003- (which favours runoff) is much more frequent than the 20% of 04570/GLO) and PREVEA (CGL2007-63258/BOS), both cases that Kidron (2015) found under the canopy at Nizana funded by the Spanish National Plan for RD&I and by the (Israel). This occurs because the canopies of these species are European ERDF Funds (European Regional Development less dense or more separated from the ground. Fund), and continued during the project SCIN (Soil Crust In- We found a positive relationship of mRL with slope, con- terNational, PRI-PIMBDV-2011-0874, European project of sistent in time and space in Cyano and Squam. This agrees with ERA-NET BIODIVERSA, the Spanish team being funded by Chamizo et al. (2012b), who found, in the same study area, that the Spanish Ministry of Economy and Competitiveness). The the effect of slope might be irrelevant at the microplot scale, but work was finally supported and culminated by the DINCOS is important at the small hillslope scale. However, the effect of project (CGL2016-78075-P, Spanish State Programme for slope was mainly due to the S2 plot. This slope effect is logical Scientific Research) and by the European ERDF Funds (Euro- but its significance is relatively unexpected here due to (i) the pean Regional Development Fund). Consuelo Rubio’s partici- opposite effect of the vegetation in the Lepra plots; and, (ii) the pation was possible thanks to the contract as a doctoral student relatively higher RC of the Cyano biocrust (Alexander and FPU18 / 00035. Dr. Javier Barbero advised us on mathemati- Calvo, 1990; Chamizo et al., 2012a) having plots of lower cal issues. steepness. Cerdá and García-Fayos (1997) found a positive Special thanks: This research was kindly facilitated by the relationship between slope and runoff initiation and sediment Viciana brothers, landowners of the El Cautivo field site. yield, but not between slope and runoff volume. The effect of the catchment area was significant, despite the REFERENCES effective contributing area in most plots usually being much smaller than the topographic one. 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Journal

Journal of Hydrology and Hydromechanicsde Gruyter

Published: Dec 1, 2021

Keywords: Semiarid; Biological soil crust; Runoff connectivity; Length slope factor; Infiltration; Tabernas Desert

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