Witold Bagniewski
email: wbagniewski@lmd.ipsl.fr

Denis-Didier Rousseau

Michael Ghil

PaleoJump: A database for abrupt transitions in past climates

Tipping points (TPs) in Earth's climate system have been the subject of increasing interest and concern in recent years, given the risk that anthropogenic forcing could cause abrupt, potentially irreversible, climate transitions. Paleoclimate records are essential for identifying past TPs and for gaining a thorough understanding of the underlying nonlinearities and bifurcation mechanisms. However, the quality, resolution, and reliability of these records can vary, making it important to carefully select the ones that provide the most accurate representation of past climates. Moreover, as paleoclimate time series vary in their origin, time spans, and periodicities, an objective, automated methodology is crucial for identifying and comparing TPs. To address these challenges, we introduce the open-source PaleoJump database, which contains a collection of carefully selected, high-resolution records originating in ice cores, marine sediments, speleothems, terrestrial records, and lake sediments. These records describe climate variability on centennial, millennial and longer time scales and cover all the continents and ocean basins. We provide an overview of their spatial distribution and discuss the gaps in coverage. Our statistical methodology includes an augmented Kolmogorov-Smirnov test and Recurrence Quantification Analysis; it is applied here, for illustration purposes, to selected records in which abrupt transitions are automatically detected and the presence of potential tipping elements is investigated. These transitions are shown in the PaleoJump database along with other essential information about the records, including location, temporal scale and resolution, as well as temporal plots. This open-source database represents, therefore, a valuable resource for researchers investigating TPs in past climates.

Introduction and Motivation

Since the discovery of Dansgaard-Oeschger (DO) events in Greenland ice cores [START_REF] Dansgaard | A new Greenland deep ice core[END_REF][START_REF] Johnsen | Irregular glacial interstadials recorded in a new Greenland ice core[END_REF][START_REF] Grootes | Comparison of oxygen isotope records from the GISP2 and GRIP Greenland ice cores[END_REF] , climate research has aimed to identify other examples of centennial-to-millennial climate variability, including in marine and terrestrial paleoclimate records [START_REF] Shackleton | Phase relationships between millennial-scale events 64,000-24,000 years ago[END_REF][START_REF] Genty | Precise dating of Dansgaard-Oeschger climate oscillations in western Europe from stalagmite data[END_REF] , and to gain insight into the mechanisms behind these changes. Many such records exhibit abrupt transitions, raising the question of whether similarly drastic changes may occur in the near future, as anthropogenic global warming pushes the climate system away from the relatively stable state that has persisted throughout the Holocene. Many of Earth's subsystems exhibit intrinsic variability and respond nonlinearly to various natural and anthropogenic forcings [START_REF] Ghil | Topics in Geophysical Fluid Dynamics: Atmospheric Dynamics, Dynamo Theory, and Climate Dynamics[END_REF][START_REF] Ghil | The physics of climate variability and climate change[END_REF] . Hence, any of these subsystems could experience a sudden shift into a new state once certain key thresholds, known as tipping points (TPs), are crossed [START_REF] Pearce | With Speed and Violence: Why Scientists Fear Tipping Points in Climate Change[END_REF][START_REF] Lenton | Tipping elements in the Earth's climate system[END_REF][START_REF] Scheffer | Early-warning signals for critical transitions[END_REF] .

Identifying potential TPs in the climate system requires theoretical and modeling work, including comparison with observations. Proxy records of past climate and environmental changes play a crucial role, by enabling the reconstruction of Earth's climatic history. These records, particularly those that show abrupt transitions, may provide valuable insights into the past behavior of Earth's systems and possible TPs. By using this information, we can gain a better understanding of the possible trajectories of future climate change and their environmental impacts.

With tens of thousands of paleoclimate datasets available, finding and selecting the most relevant records for studying past climate can be overwhelming. These proxy datasets originate from different geologic structures, contain different variables, and span a wide range of age intervals with different resolutions. In addition, due to the varying resolution and dating methods used for these records, it is important to assess their reliability. There have been efforts in recent years to build compilations of high-quality paleoclimate data, such as the ACER database of pollen and charcoal records from the last glacial period [START_REF] Sánchez Goñi | The ACER pollen and charcoal database: a global resource to document vegetation and fire response to abrupt climate changes during the last glacial period[END_REF] , the SISAL database of speleothem isotope records [START_REF] Atsawawaranunt | The SISAL database: a global resource to document oxygen and carbon isotope records from speleothems[END_REF] , the PalMod compilation of marine sediment data covering the last glacial-interglacial cycle [START_REF] Jonkers | Integrating palaeoclimate time series with rich metadata for uncertainty modelling: strategy and documentation of the PalMod 130k marine palaeoclimate data synthesis[END_REF] , the World Atlas of late Quaternary Foraminiferal Oxygen and Carbon Isotope Ratios [START_REF] Mulitza | World Atlas of late Quaternary Foraminiferal Oxygen and Carbon Isotope Ratios[END_REF] , and the PhanSST database of Phanerozoic sea surface temperature proxy data [START_REF] Judd | The PhanSST global database of Phanerozoic sea surface temperature proxy data[END_REF] . These compilations, however, are typically limited to a specific type of proxy or time interval.

To fully understand TPs, which can affect various components of the earth system [START_REF] Ghil | Topics in Geophysical Fluid Dynamics: Atmospheric Dynamics, Dynamo Theory, and Climate Dynamics[END_REF][START_REF] Lenton | Tipping elements in the Earth's climate system[END_REF][START_REF] Ghil | Hilbert problems for the geosciences in the 21st century[END_REF] and have occurred at different times in the past, it is essential to examine a diverse range of paleoclimate data. This includes marine, terrestrial, and ice records from different time intervals during which abrupt climate change events have occurred, such as the Paleocene-Eocene Thermal Maximum (PETM), DO events, and the Younger Dryas. Furthermore, as tipping elements -the subsystems that may be subject to tipping -are interconnected, a potential for domino effects exists [START_REF] Wunderling | Interacting tipping elements increase risk of climate domino effects under global warming[END_REF] . To identify and describe such effects in past records, one needs coverage from different types of archives with a comprehensive geospatial distribution.

The purpose of this paper is to address these challenges by presenting the open-source PaleoJump database 18 , https://paleojump.github.io, which compiles globally sourced high-resolution paleoclimate records that contain abrupt transitions.

The records originate in ice cores, marine sediments, speleothems, terrestrial deposits, and lake sediments, and can provide valuable information for modeling and predicting critical TPs in current and future climate evolution. The database is designed as a website, allowing easy access and navigation. It includes a map of the paleoclimate records, as well as tables that list supplementary information for each record, along with dates of the detected transitions.

In addition to providing a description of the PaleoJump database, we demonstrate its potential use by conducting a TP analysis of seven records selected from the database. Since paleoclimate records vary in their origin, time spans, and periodicities, an objective, automated methodology is key for identifying and comparing TPs. Here, we apply a recently developed method to detect abrupt transitions based on an augmented Kolmogorov-Smirnov (KS) test [START_REF] Bagniewski | Automatic detection of abrupt transitions in paleoclimate records[END_REF] to the selected records.

The KS test results are then compared with those of recurrence quantification analysis (RQA) [START_REF] Eckmann | Recurrence plots of dynamical systems[END_REF][START_REF] Marwan | Recurrence plots for the analysis of complex systems[END_REF] to further assess the validity of the findings.

The next section describes the database itself, followed by a section summarizing the KS and RQA methods. Next, a section illustrates the application of these two methods to the seven selected records, including comparisons between the results for distinct records. The following section compares the results of the two methods and provides an interpretation of our findings.

Conclusions of the work follow in the last section.

Database sources

The PaleoJump database currently includes records from 131 sites, grouped by their geological type: 49 marine-sediment cores, 32 speleothems, 18 lake sediment cores, 20 terrestrial records, and 12 ice cores. The main sources for this database are the PANGAEA and NCEI/NOAA open-access data repositories, while some records are, unfortunately, available only on request from the authors of the original studies; in the latter case, links to the corresponding articles are provided. The paleorecords have been selected for their ability to represent different aspects of past climate and environmental variability. In addition to containing abrupt transitions, these records are characterized by high temporal resolution, multi-millennial time scales, and a comprehensive spatial coverage. This selection simplifies the search for records that are most helpful in the investigation of critical transitions and of the behavior of tipping elements.

Resolution is a crucial factor in the selection of records. As a metric, we use 'maximum resolution', which we define as the temporal resolution of the 10 ky interval with the smallest average time step. We took this approach to ensure that records with nonuniform resolution or with gaps in the data are not overlooked. To make the selection more conservative, we only considered resolution for time intervals older than 14 ka BP because more recent intervals often have a significantly higher resolution. The selection criteria varied depending on the source type and time interval. For example, for records that only cover the Last Glacial Cycle, we select those with a maximum resolution of 200 years or better, while older records in our database have a resolution no worse than 400 years. However, exceptions were made for records from undersampled regions, such as the Guliya ice core [START_REF] Thompson | Tropical climate instability: The last glacial cycle from a Qinghai-Tibetan ice core[END_REF] and several lake sediment records, and for exceptionally long and complete records, like the CENOGRID [START_REF] Westerhold | An astronomically dated record of Earth's climate and its predictability over the last 66 million years[END_REF] and Chinese Loess Plateau 24 stacks. While many of the paleosites listed in PaleoJump include multiple proxy types, we have focused on proxies that can be directly compared with climate models: oxygen isotopes reflecting changes in past temperatures, sea level, and precipitation; carbon isotopes containing information on past vegetation and the carbon cycle; aeolian deposits that include signatures of past precipitation, mineral aerosols, and atmospheric transport patterns; as well as other proxy-based estimates of past temperatures.

We have mainly focused on the Last Glacial Cycle, due to the well-established evidence of past abrupt transitions -such as DO and Heinrich events -with most records also covering Holocene deglaciation. Other records extend further back in time, including DO-like events during earlier glacial cycles of the Quaternary, and earlier climatic events of the Cenozoic era, such as the Eocene-Oligocene Transition at 34 Ma or the PETM at 56 Ma. While PaleoJump provides global coverage with records from all continents and ocean basins, its spatial coverage is biased towards the North Atlantic region due to greater availability and to the strong impact of the DO events.

The well-known uncertainties in paleoclimate records need to be considered in building such a database. A key source of uncertainty is in their chronologies, as dating methods such as radiocarbon dating and layer counting have limitations and 2/22 potential sources of error [START_REF] Boers | A complete representation of uncertainties in layer-counted paleoclimatic archives[END_REF][START_REF] Goswami | Abrupt transitions in time series with uncertainties[END_REF] . When independent dating is unavailable, "wiggle matching" is often performed to match records with other, well-dated records, but this method's use can be complicated by differences in local climate variability and time lags in climate signal propagation [START_REF] Blunier | Timing of millennial-scale climate change in Antarctica and Greenland during the last glacial period[END_REF][START_REF] Skinner | An Atlantic lead over Pacific deep-water change across Termination I: implications for the application of the marine isotope stage stratigraphy[END_REF] . Additionally, recorded values of climate proxies may be affected by extra-climatic processes -physical, biological, and chemical -or by measurement errors. Interpretation of proxy records can also be challenging because a given proxy variable may be influenced by multiple climatic processes [START_REF] Shackleton | Oxygen isotope analyses and Pleistocene temperatures re-assessed[END_REF][START_REF] Mcdermott | Palaeo-climate reconstruction from stable isotope variations in speleothems: a review[END_REF][START_REF] Bagniewski | Quantification of factors impacting seawater and calcite δ 18 O during Heinrich Stadials 1 and 4[END_REF] , making it difficult to determine the specific climate conditions it represents.

In many of the records in PaleoJump, the chronology used for the original study has since been updated in more recent ones. When this is the case, we use the most recent age model's chronology. However, when the newer chronology does not cover the complete record, which is often the case, we use the older chronology. Furthermore, we did not attempt to harmonize and synchronize the age models among the records. These choices ensure that the most complete versions of the records are included in the database, while also allowing users to independently reproduce our analyses without having to reevaluate how harmonization was performed.

Five tables show the information for each record in the PaleoJump database and are included in the Supplementary Information [START_REF] Shackleton | Phase relationships between millennial-scale events 64,000-24,000 years ago[END_REF][START_REF] Genty | Precise dating of Dansgaard-Oeschger climate oscillations in western Europe from stalagmite data[END_REF][START_REF] Sánchez Goñi | The ACER pollen and charcoal database: a global resource to document vegetation and fire response to abrupt climate changes during the last glacial period[END_REF][START_REF] Thompson | Tropical climate instability: The last glacial cycle from a Qinghai-Tibetan ice core[END_REF][START_REF] Westerhold | An astronomically dated record of Earth's climate and its predictability over the last 66 million years[END_REF][START_REF] Sun | Astronomical timescale and palaeoclimatic implication of stacked 3.6-myr monsoon records from the chinese loess plateau[END_REF] .

Applying the KS test and RQA to TP identification

Given the diversity of the proxy records in the PaleoJump database, an objective, automated methodology is crucial for identifying and comparing TPs. Bagniewski et al. [START_REF] Bagniewski | Automatic detection of abrupt transitions in paleoclimate records[END_REF] formulated an augmented KS test, which they used to robustly detect and identify abrupt transitions during the last glacial cycle. These results were compared with results obtained using RQA, showing that the two methods are complementary, with KS test being more useful at detecting individual jumps and determining their exact dates, while RQA can help establish important transitions in a record's characteristic time scale. Here, we apply these two methods to a selection of records from the PaleoJump database and demonstrate the ability of the augmented KS test to accurately identify transitions in various types of paleoclimate records. the window length w being used, D KS is calculated for different w's, varying between w min and w max . The values of the latter two parameters bracket the desired time scale at which a given paleorecord is to be investigated. Furthermore, smaller jumps in the time series may be the result of an error in the observed data or small-scale variability that occurs over time intervals shorter than the sampling resolution of the proxy record and they should be discarded. Thus, for a transition to be considered significant, the change in magnitude between the two samples (i, j) should exceed a threshold σ c in their standard deviations (σ i , σ j ). Finally, as the KS test requires a large enough sample size to be significant, its results are rejected if either of the two samples has a size n smaller than n c .

At a time step at which all three conditions based on the parameters D c , σ c , and n c are satisfied, an abrupt transition is identified. As the dates of such transitions often occur in clusters, the precise date for a transition within such a cluster is determined by the maximum D KS value found within the corresponding time interval. When the maximum D KS over a given interval is shared by several time steps, the one corresponding to the maximum change in absolute magnitude is used; moreover, if there are several jumps of equal amplitude, then the one with the earliest date is used.

As the same transition may be found at slightly different dates depending on the window length that is used, we first identify the transitions detected with the longest window, which, given the larger sample size it accommodates, is the most statistically significant one. These transitions are then supplemented by those detected for the next-longest window and eventually for all other window lengths. For window w i , we discard transitions identified at time t if the interval {tw i ≤ t ≤ t + w i } contains transitions that were previously identified with a greater window length. Finally, to identify transitions between dominant climate modes, such as the Stadial-Interstadial (GS -GI) boundaries, we use a running window to extract the upper and lower values from the time series and locate the transitions that mark a shift from one mode to the other.

The parameters D c and σ c are initially optimized following receiver operating characteristic analysis 177,178 , and abrupt transitions so identified for the NGRIP ice core δ 18 O record are further compared with the change points identified using visual inspection by Rasmussen et al. 131 .

Recurrence Quantification Analysis (RQA). The KS test results are next compared with RQA results [START_REF] Eckmann | Recurrence plots of dynamical systems[END_REF][START_REF] Marwan | Recurrence plots for the analysis of complex systems[END_REF]179 . Here, the Recurrence Plot (RP) for a time series {x k : k = 1, . . . , K} is given by a square pattern in which both axes represent time. A dot is entered into a position (i, j) of the matrix R when |x ix j | < ε, with ε being the recurrence threshold. Thus, the RP appears as a square matrix R of dots. For details on how ε is determined, see Marwan et al. [START_REF] Marwan | Recurrence plots for the analysis of complex systems[END_REF] and Bagniewski et al. [START_REF] Bagniewski | Automatic detection of abrupt transitions in paleoclimate records[END_REF] .

Eckmann et al. [START_REF] Eckmann | Recurrence plots of dynamical systems[END_REF] showed that purely visual RP typologies provide useful information about a time series. However, RQA allows for a more objective way of inferring recurrence [START_REF] Marwan | Recurrence plots for the analysis of complex systems[END_REF]179 , by quantifying selected recurrence characteristics. One of the simplest RQA criteria is the recurrence rate (RR), namely the density of dots within the recurrence plot: RR describes the probability of states of the system recurring within a particular time interval. By evaluating RQA measures such as RR in a sliding window, it is possible to identify changes in the time series. Low RR values correspond to an unstable behavior of the system, and hence abrupt transitions in a time series may be identified by local RR minima.

An important advantage of the recurrence method is that it does apply to dynamical systems that are not autonomous, i.e., that may be subject to time-dependent forcing [START_REF] Eckmann | Recurrence plots of dynamical systems[END_REF] . The latter is certainly the case for the climate system in general [180][181][182][183] and, in particular, on the time scales of 10-100 kyr and longer, which are affected strongly by orbital forcing 184 .

For a more comprehensive description of both the augmented KS test and RQA, see Bagniewski et al. [START_REF] Bagniewski | Automatic detection of abrupt transitions in paleoclimate records[END_REF] .

Examples of usage

Here we show the results of the augmented KS test methodology [START_REF] Bagniewski | Automatic detection of abrupt transitions in paleoclimate records[END_REF] , as applied to records of different timescales, resolutions, and periodicities. Plots of the detected transitions, along with files listing their dates are included in the PaleoJump database;

the same is available for other records as well.

Methodology. We apply the augmented KS test to six records, given in Table 1, from each of the proxy types listed in Supplementary Tables 12345. In addition to these six records, we include the results obtained for the NGRIP ice core, which have been published in Bagniewski et al. [START_REF] Bagniewski | Automatic detection of abrupt transitions in paleoclimate records[END_REF] , and compare the latter with the three records of the last glacial cycle in the table, to wit MD03-2621, Paraiso Cave, and ODP893A. [START_REF] Bagniewski | Automatic detection of abrupt transitions in paleoclimate records[END_REF] , ordered by geological type and temporal scale; the nature of the records is indicated in the last column by the abbreviations ben = benthic, pla = planktonic, and TIC = Total Inorganic Carbon.

The KS test parameters vary depending on a record's time resolution and on the length of its age interval. For the records covering the last glacial cycle (MD03-2621, Paraiso Cave, and ODP893A), we use the same parameter values as used for the NGRIP record in Bagniewski et al. [START_REF] Bagniewski | Automatic detection of abrupt transitions in paleoclimate records[END_REF] , i.e., D c = 0.77, σ c = 1.9, n c = 3, w min = 0.1 kyr, and w max = 2.5 kyr. For the records spanning longer time intervals with a lower temporal resolution, we use longer window lengths w min and w max , thus shifting the focus of our analysis to longer time scales. For the U1308 benthic δ 18 O and Lake Ohrid TIC records, we use a w-range of 2 kyr to 20 kyr. This allows us to focus on the glacial-cycle variability, as the record's resolution is too low to properly identify DO events, particularly for data older than 1.5 Ma BP, when the U1308 record's resolution is lower than for more recent data. For the CENOGRID record, we perform two separate analyses, one with a w-range of 1 Myr to 4 Myr to determine the Quaternary's major climatic shifts, and one with a w-range of 0.02 Myr to 2.5 Myr, which covers the orbital time scale.

Note that, in paleoclimate studies, one distinguishes between units of absolute time, such as kyr or Myr, and units of age, such as ka BP or Ma BP, where 'BP' stands for "before present."

Results for Individual records. We chose the MD03-2621 reflectance record from the Cariaco Basin in the Caribbean for having a very high resolution and for its importance in studying the effect of DO events on the migrations of the intertropical convergence zone (ITCZ). The record is shown in Fig. 2 and it has been used previously to assess teleconnections between the North Atlantic basin and the Arabian Sea [START_REF] Deplazes | Links between tropical rainfall and North Atlantic climate during the last glacial period[END_REF] . When the ITCZ migrates southward during stadials, northeasterly Trade winds lead to upwelling of cool, nutrient-rich waters in the Caribbean; as the ITCZ migrates northward during interstadials, heavy convective rainfall leads to increased runoff from South America's north coast, delivering detrital material to the Cariaco Basin [START_REF] Deplazes | Links between tropical rainfall and North Atlantic climate during the last glacial period[END_REF]185 . As a result, the color reflectance in the core alternates between light-colored sediments, rich in foraminiferal carbonate and silica, and darker sediments abundant in detrital organic carbon. These changes in the marine sediments are proxies for the prevailing atmospheric circulation regime, and the meridional position of the ITCZ in the region, which are both linked to the glacial-interglacial variability.

For the KS analysis, a 20-year moving average of the MD03-2621 record is calculated in order to align its resolution with that of the NGRIP record. Our analysis does identify the "classical" DO events, as seen in the NGRIP record [START_REF] Bagniewski | Automatic detection of abrupt transitions in paleoclimate records[END_REF]131 . There is, however, no direct relationship in the identified longer-scale warm (grey bars) and cool intervals: For instance, some events appear to be merged in Fig. 2, e.g., GI-23 and 22, GI-16 and 15, GI-14 and 13, GI-10 and 9, and GI-4 and 3, while some events detected here, between 68 and 66 ka BP, are not identified in NGRIP, and GI-2 is much longer than in NGRIP.

The RQA analysis [START_REF] Marwan | Recurrence plots for the analysis of complex systems[END_REF]179 , shown in Fig. 3, does identify the major transitions in the MD03-2621 reflectance record, including the relative significance of each. It does not, however, resolve smaller transitions that occur at the centennial time scale. Please see Bagniewski et al. [START_REF] Bagniewski | Automatic detection of abrupt transitions in paleoclimate records[END_REF] for the explanation of the recurrence rate used to identify the transitions in the figure's panel (c).

The CENOGRID stack of benthic δ 18 O 23 shown here in Fig. 4 is a highly resolved 67 Myr composite from 14 marine records. Westerhold et al. [START_REF] Westerhold | An astronomically dated record of Earth's climate and its predictability over the last 66 million years[END_REF] distinguished four climate states -Hothouse, Warmhouse, Coolhouse, and Icehouse -in this record, largely following changes in the polar ice volume. The composite in the figure [START_REF] Westerhold | An astronomically dated record of Earth's climate and its predictability over the last 66 million years[END_REF] reconstructs in detail Earth's climate during the Cenozoic era, at a higher time resolution than the earlier compilation of Zachos and colleagues 186 .

Our KS analysis in Fig. 4a uses a window width 1≤ w ≤4 Myr and it identifies four major transitions towards higher The fourth transition, at 34 Ma, is the Eocene-Oligocene Transition, the sharp boundary between the warm and the hot climatic conditions in the earlier Cenozoic and the Coolhouse and then Icehouse conditions prevailing later on 187 . As this transition marks a major shift in the Earth's climate dynamics, it is a candidate for a major TP in Earth's climate history 188 . The fifth transition, at 14 Ma BP, ends a rather stable climate interval between 34 Ma and 14 Ma, characterized by the build up of the East Antarctic ice sheet 189,190 . This transition also marks the start of an increasing trend in benthic δ 18 O values 191, 192 . The final transition marks the start of the Icehouse world and it is characterized by the emergence and development of the Northern Hemisphere ice sheets.

Using a reduced window length on the last 26 Myr of the CENOGRID benthic record, many more abrupt transitions are detected in Fig. 4b. In particular, higher variability in the δ 18 O signal and much more frequent transitions are found during two [START_REF] Bagniewski | Automatic detection of abrupt transitions in paleoclimate records[END_REF] , with colors indicating the direction of the jumps. In this figure, red lines represent a warming event, while blue lines represent a cooling event. In other figures, the meaning of the colors may vary. Grey bars denote warm episodes. Note that all time axes in this paper follow the geological custom of pointing into the past. transitions, respectively. The former one of the two intervals with many jumps includes the Quaternary Period, which started 2.6 Myr ago and is well known for its high climate variability, due to the presence of large ice masses in the system [START_REF] Ghil | Topics in Geophysical Fluid Dynamics: Atmospheric Dynamics, Dynamo Theory, and Climate Dynamics[END_REF]193 .

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The interval 20-13 Ma BP, on the other hand, coincides with the exclusive use of the U1337 and U1338 records in constructing the CENOGRID stack, both of which are located in the eastern tropical Pacific. Higher sedimentation rates in these two cores might contribute to the higher variability δ 18 O observed in the stack record over this interval. For transitions detected with the shorter window for the entire CENOGRID stack, please see Fig. S1 in the Supplementary Information. The δ 18 O record from the Paraiso Cave in the Amazon rainforest reveals a relationship between shifts in global temperature and changes in rainfall patterns in the region; see Fig. 5. The record shows that the Amazon basin experienced drier conditions during the last glacial period, most probably due to the lower temperatures. The record exhibits reduced precipitation during DO interstadials and increased precipitation during stadials, a pattern that negatively correlates with Chinese speleothem records [START_REF] Cheng | The Asian monsoon over the past 640,000 years and ice age terminations[END_REF] , suggesting a phase opposition in rainfall between the two regions. The abrupt shifts in precipitation during DO events suggest that the Amazonian climate subsystem may exhibit bistability, making it a potential tipping element as changes in precipitation may lead to forest dieback 194 .

Results for core intercomparisons. In Fig. 6, we compare four paleorecords of different types and from distinct locations: NGRIP δ 18 O, MD03-2621 reflectance, Paraiso Cave δ 18 O, and ODP893A planktic δ 18 O from the Santa Barbara Basin.

Overall, the abrupt transitions in the four records appear to be fairly synchronous, with the main Greenland DO events from NGRIP also observed for the two marine records and the one speleothem record. The transitions that correspond to Greenland interstadials (GIs) GI-12 to GI-3 131 are identified in all four records, with only a few exceptions: GI-3 is not identified for the ODP893A record, due to an insufficient number of data points; and GI-5.1 is not identified in any record, except as a cooling Age (ka BP) event in MD03-2621 and in Paraiso cave. Also, GI-10 and GI-9 appear as a single interstadial in the Paraiso cave and ODP893A records, which is probably due to a decreased time resolution observed in both records during this time interval.

Finally, Fig. 7 shows the comparison between the U1308 benthic δ 18 O record and the Lake Ohrid Total Inorganic Carbon [START_REF] Hodell | Mode transitions in Northern Hemisphere glaciation: co-evolution of millennial and orbital variability in Quaternary climate[END_REF]196 . Here, we only show the 1.4-0 Ma BP time interval that corresponds to the length of the Lake Ohrid record. For the full 3.1 Myr U1308 record, please see Fig. S2 in the Supplementary Information. The Lake Ohrid TIC record in Fig. 7b shows glacial-interglacial variability in biomass over the past 1.4 Myr. Here, our KS analysis shows numerous abrupt transitions towards high TIC intervals that correspond to interglacial episodes, as well as matching ones of opposite sign. The interglacials are associated with forested environmental conditions that are consistent with odd-numbered MISs, as was the case for the U1308 record in the figure's panel (a). The glacial episodes, to the contrary, correspond to forestless conditions, that, according to the available timescale, are consistent with even-numbered MISs.

Discussion

The two methods. The augmented KS test of Bagniewski et al. [START_REF] Bagniewski | Automatic detection of abrupt transitions in paleoclimate records[END_REF] has detected abrupt transitions on different time scales in a variety of paleorecords. These include the NGRIP ice core, the Paraiso Cave speleothem, and the MD03-2621 and ODP893A marine sediment cores for the last glacial cycle; the U1308 marine sediment core and Lake Ohrid TIC for the Middle and Late Pleistocene; and the CENOGRID marine sediment stack for the Cenozoic Era. While possible mechanisms giving rise to the observed variability in these records have been discussed in previous studies, the objective, precise and robust dating of the main transitions using the augmented KS test may allow a more detailed and definitive analysis and modeling.

The transitions identified for the MD03-2621 reflectance record with the RQA methodology [START_REF] Eckmann | Recurrence plots of dynamical systems[END_REF][START_REF] Marwan | Recurrence plots for the analysis of complex systems[END_REF]179 do correspond to a subset of those found with the KS test, but several smaller-scale transitions identified by the latter have not been found with the former method. As discussed in Bagniewski et al. [START_REF] Bagniewski | Automatic detection of abrupt transitions in paleoclimate records[END_REF] , recognizing the transition points by RQA becomes increasingly difficult at time scales shorter than the window length. The RQA approach, though, does allow one to quantify the magnitude of each transition, and it may thus be useful for identifying key transitions. Moreover, RPs may be helpful in illustrating changes in periodicity.

Interpretation of findings. The high-resolution MD03-2621 reflectance record from the Cariaco Basin 64 in Fig. 2 shows abrupt transitions that are largely in agreement with those detected by our KS test for the NGRIP record. Desplazes et al. [START_REF] Deplazes | Links between tropical rainfall and North Atlantic climate during the last glacial period[END_REF] have argued that these transitions are driven by the ITCZ displacements that occurred primarily in response to Northern Hemisphere temperature variations. These authors indicated that the ITCZ migrated seasonally during mild stadials, but was permanently displaced south of the Cariaco Basin during the colder stadial conditions. The very high resolution of the MD03-2621 record allows a detailed comparison with the transitions identified for the NGRIP record. The fact that several small-scale NGRIP transitions are not identified by our KS test in the MD03-2621 record suggests that a TP linked to ITCZ migration was not crossed during these events. Furthermore, the KS test does reveal transitions that have not been recognized previously in either record 131 , e.g., at 86.15 ka BP, which we find in both the NGRIP and MD03-2621 records.

In the 67-Myr CENOGRID stack (Fig. 4) of benthic δ 18 O [START_REF] Westerhold | An astronomically dated record of Earth's climate and its predictability over the last 66 million years[END_REF]186 , we identified four major cooling transitions that culminate with the start of the Pleistocene, as well as two warming transitions, including the PETM. These major jumps agree with those identified in Westerhold et al. [START_REF] Westerhold | An astronomically dated record of Earth's climate and its predictability over the last 66 million years[END_REF] . However, using a shorter window length, many more transitions were detected during the Pleistocene, well known for its higher climate variability [START_REF] Ghil | Topics in Geophysical Fluid Dynamics: Atmospheric Dynamics, Dynamo Theory, and Climate Dynamics[END_REF]193 , as well as during the early Miocene, i.e., between the Oligocene-Miocene transition at 23 Ma BP [198][199][200] and the mid-Miocene transition at 14 Ma BP 190 . A possible reason is the fact that the 20-13 Ma BP interval in the stack has been constructed using records from the eastern Tropical Pacific. This region has been characterized by high upwelling rates and sedimentation rates in the past 201 . While the CENOGRID composite has 11/22 a uniform resolution, higher sedimentation rates could affect the resolution of the original records and, therewith, even the variability seen in lower-resolution sampling.

It follows from these remarks on Figs. 4(a,b) that variations in resolution of the data, which can arise from various factors including measurement techniques and source region characteristics, can have a considerable effect on the frequency of detected transitions. These factors can significantly impact the reliability of transition detection methods, thus highlighting the need for caution when using individual records as proxies for global climate. While statistical indicators allow us to quantify jumps in the data without any climatic context being provided, it is important to consider the limitations of such an approach, and to supplement it with an independent understanding of the proxy data whenever possible. By doing so, we can better contextualize and understand the implications of these jumps.

The Paraiso Cave record 165 from the eastern Amazon lowlands in Fig. 5 shows drier conditions during interglacials, with abrupt transitions matching those that correspond to the DO events identified in the NGRIP ice core record. The Amazon record is also in fairly good agreement with the nearby MD03-2621 marine sediment record. Notably, several of NGRIP's DO events appear combined in both records, namely GI-5.2 and GI-5.1, as well as GI-10 and GI-9, which might indicate that a climate change event over Greenland did not trigger a tipping event in the Amazon basin. Alternatively, the first merging may question the separation of the classical GI-5 event 202 into two distinct events, 5.2 and 5.1.

The comparison of four records on the same time scale in Fig. 6 demonstrates that a signal of abrupt climate change is detected when using the KS method with similar accuracy for different types of paleodata. The differences in the dates of the transitions may be largely explained by the use of different age models in each of the records, with MD03-2621 fine-tuned to the NGRIP chronology, and ODP893A fine-tuned to the GISP2 chronology, while the NGRIP and Paraiso Cave records were independently dated. Notably, ODP893A data prior to GI-8 appear misaligned with the other three records. The chronology of jumps in ODP893A indicates that the warm interval between 42.4 ka BP and 40.8 ka BP may correspond to an event spanning GI-10 and GI-9, while the warm interval between 45.3 ka BP and 43.3 ka BP may correspond to GI-11.

It is important to keep in mind that age estimates of many paleoclimate records, including some of those discussed here, are often not determined through independent methods, but rather are "tuned" or wiggle-matched to other records, such as the global benthic δ 18 O stack 197 or the NGRIP δ 18 O record 131 . As the abrupt jumps in these records are themselves used as tie-points, it is expected that the KS test would show a similarity in the timing of jumps in records that were tuned to the same reference record. Therefore, any differences in the timing of transitions between these records should not be taken as indicative of the chronology of events, but rather as a result of differences between the KS method and the transition detection method used in the wiggle matching process. This fact should be taken into consideration when comparing records that have not been independently dated.

In addition to the classical GI transitions, several additional jumps are identified in each of the marine and cave records.

These jumps may be the representative of local climate changes or, in some cases, be artifacts of sampling resolution or measurement error. Stronger evidence for a local or regional event may be obtained when comparing two nearby records, like the Paraiso Cave in the Amazon and the MD03-2621 marine record from the Cariaco Basin. In both records, the start of GI-5.2 is represented as two warming transitions, in contrast with the NGRIP and ODP893A records, where only one sharp transition is present. Likewise, the end of GI-9 in the two tropical, South American records appears as two successive cooling events.

These results point to the potential of using the KS method to improve fine-tuning the synchroneity of two or more records, when an independent dating method is not available.

The comparison in Fig. 7 of KS-detected transitions in marine core U1308 [START_REF] Hodell | Mode transitions in Northern Hemisphere glaciation: co-evolution of millennial and orbital variability in Quaternary climate[END_REF] and in Lake Ohrid TIC 137 identifies the transitions between individual glacials and interglacials. In the two records, the transitions are well identified, despite the resolution of the two being different, and they offer a precise dating for the chronology of the past glacial cycles. The transitions are overall in good agreement between the two records. Still, the warm events in Lake Ohrid are essentially atmospheric and thus have often a shorter duration than in the marine record, while cooling transitions precede those in the deep ocean by several thousand years. This could indicate that a significant time lag is present, either in ice sheet growth in response to atmospheric cooling, or in the propagation of the cooling signal into the deep North Atlantic.

Furthermore, there are atmospheric interglacial episodes missing in the oceanic U1308 record. This mismatch between the lake record 137 and the marine one 95 could be attributed to the fact that the KS test does sometimes find more transitions in one record than in another one, even for the same type of proxy and within the same region. Such occurrences may be due to the local environment, the sampling method, or some aspect of the KS method itself. When this is the case, it is importantalthough not always feasible -to obtain additional records covering a similar time interval with a similar resolution, in order to shed further light on the mismatch between the two original records. It should be noted that this study analyzed only one proxy type from each location. A more comprehensive representation of past transitions could be achieved by investigating different proxy records from the same core. For example, in contrast to the Rasmussen et al. 131 study of the NGRIP record, which analyzed both the δ 18 O and Ca 2+ proxies, this study only utilized δ 18 O (Fig. 6a), which is a likely reason for not detecting the GI-5.1 event.

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Concluding remarks

The The examples given in the paper on abrupt-transition identification demonstrate the usefulness of the records included in PaleoJump for learning about potential tipping events in Earth's history and for comparing such events across different locations around the world. The accessibility of such high-quality records is an invaluable resource for the climate modeling community that requires comparing their results across a hierarchy of models 183,203 with observations.

We also demonstrated the usefulness of the KS test [START_REF] Bagniewski | Automatic detection of abrupt transitions in paleoclimate records[END_REF] for reconstructing the chronology of Earth's main climatic events. The newly developed tool for automatic detection of abrupt transitions may be applied to different types of paleorecords, allowing to objectively and robustly characterize the tipping phenomenon for climate subsystems already suspected of being subject to tipping [START_REF] Lenton | Tipping elements in the Earth's climate system[END_REF] , but also to identify previously unrecognized tipping elements in past climates. The observational descriptions of tipping that can be obtained from PaleoJump using our KS methodology, combined with the application of Earth System Models, can help improve the understanding of the bifurcation mechanisms of global and regional climate and identify possible TPs for future climates.

Our results also indicate that paleorecord interpretations may vary, since the abrupt transitions identified in them will depend on the time scale and type of variability that is investigated. For example, the KS method's parameters 19 may be changed when studying different proxy record resolutions, affecting the frequency and exact timing of the TPs that are identified.

The agreement in timing and pattern between jumps in distinct records can confirm the correctness of each record separately, as well as of the inferences on climate variability drawn from these jumps. Specifically, the ability of the KS method to identify matching small-scale transitions in different high-resolution records may be used to validate these transitions as being the result of genuine global or regional climatic events, as opposed to just sampling errors. Furthermore, significant differences in records that are, overall, in good agreement with each other may help decode the chronology of tipping events or an approximate range for a tipping threshold. A fortiori, the differences in timing and pattern between jumps in distinct records that we also found emphasize the importance of a consistent dating methodology.

In a potential second step, the transition detection tools presented here could be used for harmonizing and synchronizing the records of the PaleoJump database, in a way that resembles the work conducted by several research teams in recent years [START_REF] Jonkers | Integrating palaeoclimate time series with rich metadata for uncertainty modelling: strategy and documentation of the PalMod 130k marine palaeoclimate data synthesis[END_REF]159,[204][205][206][207] . Doing so would facilitate interpretating the abrupt changes in these records.

The broad spatial coverage of the PaleoJump database 18 , https://paleojump.github.io, with its records that vary in their nature -ice, marine and land -as well as in their length and resolution, will facilitate research on tipping elements in Earth's climate, including the polar ice sheets, the Atlantic Meridional Overturning Circulation, and the tropical rainforests and monsoon systems. Furthermore, it will support establishing improved criteria on where and how to collect data for reliable early warning signals of impending TPs.

Figure 1 .

 1 Figure 1. Map of the records included in the PaleoJump database and listed in the Supplementary Information. The five record sources -marine sediments, ice cores, terrestrial deposits, speleothems, and lake sediments -are identified in the legend by color.

δ 18 O

 18 values and two towards lower ones. The oldest transition, at 58 Ma BP, is characterized by a shift from the moderately warm climate prevailing at the beginning of the Cenozoic to the hot conditions marked by the Early Eocene Climate Optimum between 54 Ma and 49-48 Ma BP. The second transition corresponds to the short but intense warm event known as the PETM, the Cenozoic's hottest one. The third transition marks the end of this hot interval and the return to the milder and relatively stable conditions that prevailed between 67 Ma and 58 Ma BP.

Figure 3 .

 3 Figure 3. Recurrence Quantification Analysis (RQA) 21, 179 for the MD03-2621 reflectance record 64 . (a) Time series with vertical axis as in Fig. 2; (b) recurrence plot (RP); and (c) recurrence rate. Magenta crosses in panel (c) represent the transitions identified by the RQA.

Figure 4 .

 4 Figure 4. CENOGRID stack of benthic δ 18 O 23 . Vertical lines represent transitions detected by the KS test 19 , with colors indicating the direction of the jumps. Grey bars represent warm episodes. (a) Transitions detected for the entire record using a window w range of 1 to 4 Myr, and (b) transitions detected for the interval 26-0 Ma BP using a w range of 0.02 to 2.5 Myr; see also the earlier subsection on "Methodology." The vertical axes are reversed.

Figure 5 .

 5 Figure 5. Paraiso Cave (PAR07) δ 18 O 165 . Vertical lines represent transitions detected by the KS algorithm 19 , with colors indicating the direction of the jumps. Grey bars represent dry interglacial conditions.

(

  TIC) record over a 1.4 Myr time interval that includes multiple glacial-interglacial transitions. The U1308 benthic δ 18 O record in panel (a) of the figure is a 3.1 Myr record located within the ice-rafted detritus belt of the North Atlantic 195 . This record is a proxy for deep-water temperature and global ice volume, and it has enabled a detailed reconstruction of the history of orbital and millennial-scale climate variability during the Quaternary; it documents the changes in Northern Hemisphere ice sheets that follow the glacial-interglacial cycles, as well as mode transitions identified at 2.55 Ma, 1.5 Ma, 1.25 Ma, 0.65 Ma and 0.35 Ma BP

The 1 .

 1 25-0.65 Ma BP interval in the figure corresponds to the Mid-Pleistocene Transition, characterized by an increase in the amplitude of the glacial-interglacial fluctuations and a shift from a predominantly 40 kyr to a predominantly 100 kyr periodicity; see Reichers et al.184 and references therein. The abrupt transition at 0.35 Ma marks the start of the strongest interglacial of the record, which corresponds to the marine isotope stage (MIS) 9. Here, our KS analysis agrees with the well established marine isotope stratigraphy ofLisiecki and Raymo 197 by detecting rapid warmings that correspond to the classical terminations leading to interglacials, as well as rapid coolings that initiate glacial stages.

18 Figure 6 .Figure 7 .

 1867 Figure 6. Comparison of four paleorecords over the 45.5 -27 ka BP interval: (a) NGRIP ice core δ 18 O 131 ; (b) MD03-2621 marine sediment reflectance 64 ; (c) Paraiso Cave (PAR07) δ 18 O 165 ; and (d) ODP893A marine sediment N. pachyderma δ 18 O 87, 88 . Vertical lines represent detected transitions, with colors indicating the direction of the jumps. Grey bars in panel (a) represent interstadials identified for the NGRIP δ 18 O record by Bagniewski et al.[START_REF] Bagniewski | Automatic detection of abrupt transitions in paleoclimate records[END_REF] . Note that the "ka BP" time unit, where the 'Present' is defined as the year 1950, applies only to the Paraiso and ODP893A records. The NGRIP and MD03-2621 records use the "ka b2k" time scale, where 'b2k' refers to the year 2000 as the origin of past times. The vertical axes in panels (b) and (d) are reversed.

  carefully selected, high-quality paleoproxy records in the open-source PaleoJump database18 , https://paleojump.github.io, have different temporal scales and a global spatial coverage; see again Fig.1. These records provide an easily accessible resource for research on potential tipping elements in Earth's climate. Still, major gaps in the marine sediment records exist in the Southern Hemisphere, especially in the Indian and Pacific Oceans. Only sparse terrestrial data are available from the high latitudes in both hemispheres, due to the recent glaciation. The only data from the African continent come from two East African lake sediment records. Even though much information is at hand from the more than 100 sites listed in this paper, more records are needed to fill geographical and temporal gaps, especially in the Southern Hemisphere.

Kolmogorov-Smirnov (KS) test. The

  augmented KS methodology[START_REF] Bagniewski | Automatic detection of abrupt transitions in paleoclimate records[END_REF] is based on the nonparametric KS test175 . A two-sample KS test is applied to two neighboring samples drawn from a proxy time series within a sliding window of length w. The commonality of the two samples is quantified by the the KS statistic D KS 175, 176 . A "jump" in the time series is identified at any point in time at which D KS is greater than a cut-off threshold D c . As the KS test can give very different results depending on

	3/22

Table 1 .

 1 Records analyzed using the augmented KS test

	Type	Site name	Location	Depth/elevation Age	Res.	Proxy
	Marine	ODP893A 87, 88	34.28, -120.03	576 m	65 -0 ka	41 y	pla δ 18 O
	Marine	MD03-2621 64	10.678, -64.972 847 m	109 -6 ka	0.1 y	reflectance
	Marine	U1308 95	49.878, -24.238 3871 m	3143 -0 ka 118 y	ben δ 18 O
	Marine	CENOGRID 23	N/A	N/A	67.1 -0 Ma 2000 y ben δ 18 O
	Terrestrial Paraiso (PAR07) 165 -4.067, -55.45	60 m	45 -18 ka	21 y	δ 18 O
							4/22

Acknowledgements

We would like to express our gratitude to two anonymous reviewers whose thoughtful and constructive comments significantly improved the overall quality of the paper. This work is Tipping Points in the Earth System (TiPES) contribution #180. This study has been funded by the European Union's Horizon 2020 research and innovation programme (grant agreement No. 820970). This is LDEO contribution.

Data availability

The datasets analyzed during the current study are available through Zenodo (https://doi.org/10.5281/zenodo.6534031) 18 and on the PaleoJump website, https://paleojump.github.io. The source code of the PaleoJump website can be found on GitHub at https://github.com/paleojump/paleojump. The codes used for KS and RQA analyses are part of the TiPES statistical toolbox, available on GitHub at https://github.com/paleojump/TiPES_statistical_toolbox.

Competing interests

The authors declare no competing interests.


Ph.D Daniel A Beysens
email: daniel.beysens@espci.fr

ESTIMATING DEW YIELD WORLDWIDE FROM A FEW METEO DATA

Keywords: dew water, dew modeling, world dew estimation, radiative cooling dew water, dew modeling, world dew estimation, radiative cooling

There is a general need to determine dew yield in any place of the world. However, its determination requires systematic measurements that are not available everywhere. In addition, it depends on the particularities of the dew collector. A simple analytical formula valid for planar dew collectors is elaborated here. It is based on laboratory experiments where it is established that heat losses with surrounding air is the dominant parameter that limits dew condensation. A simple analytical formulation is then derived, which only needs cloud coverage, wind velocity, air and dew point temperatures data to be collected, at least once in a day before sunrise. The formulation is tested in several places in the world with different climates. Agreement within typically 30% is found with dew measurements. Such an analytical relationship can thus provide a useful tool to obtain a worldwide estimation of the dew potential.

Introduction

The occurrence of dew can have positive or negative aspects. Its importance for agriculture has been long recognized. Its manifestation can be negative as its deposition favors parasitic diseases caused by fungi, bacteria, viruses and other microscopic organisms [START_REF] Wallin | Dew, its significance and measurement in phytopathology[END_REF][START_REF] Aylor | A framework for examining inter-regional aerial transport of fungal spores[END_REF]. When the combination of moisture deposition on leaves and temperatures are appropriate, these diseases can cause severe damage to agricultural yields. Dew water can also be considered as an additional source of water for human and plants. During dry or intermediate seasons or in semi-arid or arid climates, dew can exhibit a beneficial role in providing naturally a supplement of water to plants [START_REF] Zangvil | Six years of dew observations in the Negev Desert, Israel[END_REF][START_REF] Malek | Dew contribution to the annual water balance in semi-arid desert valleys[END_REF][START_REF] Munné-Bosch | Diurnal variations of photosynthesis and dew absorption by leaves in two evergreen shrubs growing in Mediterranean field conditions[END_REF][START_REF] Koto N'gobi | Condensable humidity of the atmosphere in Benin: contribution to the correction of the corn hydrous stress in a semi-arid area[END_REF] and microorganisms [START_REF] Kidron | An Investigation of the Role of Water (Rain and Dew) in Controlling the Growth Form of Lichens on Cobbles in the Negev Desert[END_REF].

*Manuscript

Click here to view linked References 2 For human uses, dew can be harvested by special devices, the oldest referenced dew collectors being from the alchemists [START_REF] Flamel | Mutus Liber[END_REF]. More recently, such passive dew collection has been the object of several researches to increase the amount of collected water [START_REF] Nilsson | Initial experiments on dew collection in Sweden and Tanzania[END_REF][START_REF] Muselli | Dew water collector for potable water in Ajaccio (Corsica Island, France)[END_REF][START_REF] Jacobs | Passive dew collection in a grassland area, The Netherlands[END_REF][START_REF] Sharan | Very large dew and rain ridge collector in Kutch area ( Gujarat,India)[END_REF][START_REF] Maestre-Valero | Estimation of dew yield from radiative condensers by means of an energy balance model[END_REF]OPUR, 2015). Special surface structures have been developed, at the nano-or micro-scale (foil, paint, additives) and macroscale (shape). The beneficial role of surface edges has been recently highlighted [START_REF] Beysens | New architectural forms to enhance dew collection[END_REF]. The potential role of dew water to give access to low cost, clean fresh water has been recognized for developing countries situated within arid to sub-tropical regions where access to clean water is limited or nonexistent [START_REF] Sharan | Dew Harvest[END_REF].

Dew results from the condensation of water vapor on a surface, in contrast to fog, which is constituted of tiny (1 -40 m) water drops which form in the atmosphere and are carried by wind. Condensation can proceed on the surface because the latter cools down below the dew point temperature of surrounding air, due to the radiation deficit between surface and atmosphere. Dew therefore depends on the details of the condensation surface properties and the characteristics of the local atmospheric environment. A world dew map is still not available as dew yield depends on these both specific (substrate) and local (environment) characteristics in a manner that is still not fully precisely modelled.

All the models that have been considered are based on energy balance such as the Penman-Monteith equation (Monteith, 1957, Garratt and[START_REF] Garratt | On the contribution to dew formation[END_REF]. Cooling by radiation deficit between the surface and the atmosphere is balanced with heating by conduction (solid surface contact), convection (with surrounding air) and condensation (water latent heat of condensation). Differences appear in the evaluation of the radiation deficit (either calculated from a sky model: [START_REF] Awanou | Study of natural condensation of atmospheric humidity[END_REF] or measured with radiometers: [START_REF] Kalthoff | The energy balance, evapo-transpiration and nocturnal dew deposition of an arid valley in the Andes[END_REF][START_REF] Moro | Dew measurement by Eddy covariance and wetness sensor in a semiarid ecosystem of SE Spain[END_REF][START_REF] Maestre-Valero | Estimation of dew yield from radiative condensers by means of an energy balance model[END_REF]Ucles et al. 2013) and the convection losses estimated from mass and thermal coupling coefficient (Pedro and Gillepsie, 1982;[START_REF] Jacobs | Passive dew collection in a grassland area, The Netherlands[END_REF]. Measurements of surface temperature can also be performed as in [START_REF] Nikolayev | Water recovery from dew[END_REF]. The use of Computational Fluid Dynamics (CFD, [START_REF] Clus | Comparison of Various Radiation-cooled Dew Condensers Using Computational Fluid Dynamics[END_REF] can greatly help, especially for concave structures such as cones. However, the results are still dependent on the sky emissivity model and the thermal coupling coefficients, which makes this technique, although useful to compare different surface geometries, also subjected to uncertainties. A purely statistical approach, which uses artificial networks, has been successfully tested by [START_REF] Lekouch | Rooftop dew, fog and rain collection in southwest Morocco and predictive dew modelling using neural networks[END_REF]. Although it allows precise prediction to be made in the place where data have been obtained and analysed, its extrapolation to other places is nevertheless subjected to uncontrolled uncertainties.

A simplified model that would demand only a few regular, simple data, available everywhere in the world would then be much helpful, particularly when aiming to determine the potential dew yield in any place globally, and especially in arid or semi-arid environments. The latter often corresponds to low inhabited and/or developing countries where a network of sophisticated meteorological measurements is lacking. It appears [START_REF] Lekouch | Rooftop dew, fog and rain collection in southwest Morocco and predictive dew modelling using neural networks[END_REF]) that dew yield is strongly correlated with only a few statistically independent meteorological parameters: air temperature T a , dew point temperature T d or relative humidity RH, cloud coverage N, and wind speed V (measured at 10 m elevation, unless specified). These data are collected on a regular basis in many meteorological stations in the world (e.g. in airports) and can be easily obtained.

The goal of this study is then to provide a physical model with explicit analytical dependence of dew yield on T a , T d , N, and V. However, dew depends not only of atmospheric parameters but also on the properties and geometry of the condensing surface and in particular how the energy exchange is performed between the condenser and the atmosphere: radiation exchange and convective heat transfer. Variations of 40% between different condenser shapes can be regularly found although the meteorological parameters are rigorously the same [START_REF] Clus | Comparison of Various Radiation-cooled Dew Condensers Using Computational Fluid Dynamics[END_REF]. When the efficiency of drop collection is taken into account (scraping or not scraping, edge effects) difference of 400% can even be found [START_REF] Beysens | New architectural forms to enhance dew collection[END_REF]. One will thus consider in the following only plane condensing surfaces with emissivity unity (black body) located at 1 m above the ground and thermally isolated from it. One will also keep in mind that the local characteristics of the thermal exchange can modify the yield by 30-40%. This latter value gives the range of the possible approximations that can be made for modeling dew formation.

The paper is organized as follows. First, the basic equations are reported. Second, a laboratory experiment on water condensation is described; it leads to a unique equation giving dew yield. This equation is then adapted to natural dew formation and tested against dedicated measurements. (The present formulation has been deposited by the author in a Lettre Soleau, [START_REF] Beysens | Simplified formulations to estimate the dew yield from current data weather (air temperature, dew point temperature or relative humidity, cloud coverage, wind speed[END_REF].

Theoretical background

The determination of the dew yield requires solving a thermal problem based on an equilibrium equation between sensitive and latent heat fluxes:

  cond he i w c c R R R mc Mc dt dT    
(1)

Here T c (K) is the surface temperature of the condenser, M and m (Kg) are the masses of the condenser and of the condensate, respectively, c c and c w (J.Kg -1 . K -1 ) are the specific heats of the condenser materials and water, respectively, and t (s) is time. The variables in the right part of the equation represent the various thermal processes of heat transfer at the condenser surface: R i (W) is for cooling energy (practically less than 100 Wm -2 ), R he (W) for heat exchange with ambient air and R cond (W) for the energy gain due to the latent heat of condensation per unit of mass, L c (J.Kg -1 ). One has voluntarily omitted the conductive term of the condenser support by assuming that the condensing surface can be fixed on an adiabatic material.

The condensation and heat exchange terms can be written as:

dt dm L R c cond  (2)   c a c he T T aS R   , (3)
where a (W.K -1 m -2 ) is a coefficient of convective heat transfer. T a (K) is the temperature of the ambient air and S c (m 2 ) is the condenser surface. The parameter a is correlated with the thickness of the thermal boundary layer and depends on the air speed V (m.s -1 ) far from the plate, i.e. the windspeed of the wind if this latter is larger than that of natural convection ( 0.6 m/s, according to [START_REF] Beysens | Measurement and modelling of dew in island, coastal and alpine area[END_REF]. According to Pedro and Gillespie (1982), one can express a in a laminar flow regime as:

L V kf a  . ( 4
)
The factor f (W.K -1 .m -2 .s 1/2 ) is empirical. For a flow parallel to a plane sheet of size L = S c 1/2 , its value according to Pedro and Gillespie (1982) is f=4 WK -1 m -2 s 1/2 . A corrective factor, k, has been introduced by [START_REF] Beysens | Measurement and modelling of dew in island, coastal and alpine area[END_REF]. It is experimentally on order 3 and corresponds to a practical enhancement of heat transfer when dealing with planar condensers. The equation representing the condensed mass is described by the rate of condensation:

       negative if positive if T p T p wS dt dm c sat a a c 0 ) ( ) ( (5)
where p sat (T c ) (Pa) is the saturation water vapor pressure at condenser temperature T c (K) and p a (T a ) (Pa) is the water pressure in the humid air above the condenser. The water vapor transfer coefficient is proportional to a in Eq. 4 as it depends on the same hydrodynamic boundary layer, the values of the thermal diffusivity coefficient and the diffusion coefficient of water molecules in air being nearly equal ( 2.3×10 -5 m 2 .s -1 ). According to Pedro and Gillespie (1982):

w= 0.656a/(p 0 с а ). ( 6
)
Here p 0 is the atmospheric pressure and с а (= 1.0110 3 J. Kg -1 .K -1 ) is the specific heat of air.

Determining dm/dt requires solving Eqs. 1 and 5, which can be done by iteration (Pedro and Gillepsie, 1982) and/or by T c measurements [START_REF] Nikolayev | Water recovery from dew[END_REF]. A simplification in Eq. 3 can be made by assuming that dew starts to form at the dew point temperature (this is strictly true only for hydrophilic substrates or on geometrical or chemical surface defects, see [START_REF] Beysens | Dew nucleation and growth[END_REF]. Measurements [START_REF] Muselli | Dew water collector for potable water in Ajaccio (Corsica Island, France)[END_REF](Muselli et al. , 2006;;[START_REF] Beysens | Measurement and modelling of dew in island, coastal and alpine area[END_REF][START_REF] Lekouch | Rooftop dew, fog and rain collection in southwest Morocco and predictive dew modelling using neural networks[END_REF] indicate that T a -T d rarely exceeds  1K. Then Eq. 3 can be rewritten as

  d a c he T T aS R   , (7)
which now depends only on meteorological measurements.

Laboratory study

Experimental details

In order to take into account the important parameters of the problem, an experiment is carried out with a vertical square stainless steel plate of side L=0.2 m and thickness e = 2 mm (Fig. 1). The plate is screwed on an electrolytic copper plate of same dimensions cooled by a Peltier element. Thermal contacts Peltier -copper -steel are reinforced by thermal grease. The copper plate is thermally insulated from air by 60 mm thick Styrofoam (Fig. 1).

A power supply provide electric power P (W) to the Peltier element. It can be adjusted between 0 and 60 W within 1% accuracy. We will see just below that these powers correspond typically to typical radiative cooling power found in natural dew condensation.

The steel plate is nearly isothermal (within  0.25 K) as verified by temperature measurements performed at different places with a miniature thermocouple (0.1 K accuracy).

Temperatures of the Peltier element, T p (°C), and surface temperature, T c (°C) of the steel plate are measured by thermocouples (0.1 K accuracy) and recorded every 15 minutes with a data logger.

The use of a climatic chamber to vary air temperature and humidity is not adequate as air flows generated by fans are turbulent and uncontrolled. Therefore the experiment is performed in a small laboratory room whose window is left half open to make air temperature and humidity vary between day and night to reproduce outdoor conditions (Fig. 1). The plate is directed towards inside the room to prevent radiation cooling and to protect it from air external flows. The "wind" to which the plate is subjected is then mostly natural convection.

Tests with a cup anemometer with stalling speed 0.5 m.s -1 indeed did not measure any air flow. The parameters of the ambient air: T a , RH (%) or T d are recorded every 15 minutes by the same data logger used for T p and T c . Temperature and humidity sensors are set 15 cm away from the plate (Fig. 1) for not perturbing convective air flows around the condensing plate.

A small gutter with a V-shape is placed at the basis of the condensing plate and collects water, which flows in a beaker placed on an electronic balance. The beaker is closed by aluminum foil with small opening to prevent evaporation. The collected water mass, m, is measured every 15 minutes and data are recorded in a computer. This technique induces a small delay from the time where the water drops detach from the plate and reach the beaker. One also cannot detect very low levels of condensation, as they correspond to drops that do not detach from the surface. In terms of electric power, this threshold corresponds to P 0 ≈ 1 W.

The cooling power available at the external surface of the plate is not proportional to the electric power provided to the Peltier element. It is necessary to account for Joule effects and thermal losses of the copper plate, in spite of the thermal insulation. The useful heat flow, Q (W), for cooling and condensing at the plate surface is the heat flow from the (hot) plate external surface to the (cold) Peltier element surface. It can be evaluated by measuring the difference in temperature T a -T p in the absence of condensation. With q (W.m -2 ) the cooling power per unit surface:

  p a s p a T T a a e T T L Q q               1 2  . ( 8
)
Here  s = 14.6 W.m -1 .K -1 is the stainless steel thermal conductivity (CRC Handbook of Chemistry and Physics, 2006) and a is the thermal exchange coefficient of Eq. 4. Its value can be calculated. From [START_REF] Incropera | Fundamentals of Heat and MassTransfer[END_REF], a = a Nu/L, where  a (=0.026W.m -1 .K -1 ) is air thermal conductivity and Nu is the Nusselt number. The latter can be classically expressed for a vertical plate as a function of the Rayleigh number Ra = g a (T a -T c )L 3 /(D T )  g a (T a -T d )L 3 /(D T ) as Nu= 0.59 Ra 1/4 (Ra is in the range 10 4 -10 9 ). Here g (= 9.81 m.s -2 ) is the earth acceleration constant,  a T a +T d )  3.4 10 -3 K -1 is air thermal expansion (air is considered as an ideal gas),  -5 m 2 .s -1 ) is air dynamic viscosity and D T (=2.2  -5 m 2 .s -1 ) is air thermal diffusivity. The numerical values are from the CRC Handbook of Chemistry and Physics (2006). It follows a= 6 W.m -2 .K -1 .

The relation between q=6(T a -T d ) and P is shown in Fig. 2. The data follow approximately a log variation (this variation empirically reproduces the saturation of cooling at large flux):

P c b q ln   (9)
with b = (34 ± 2) W.m 2 and c = (23 ± 1) W, with P in W (uncertainties: one SD). The powers used, in the range P ≈ [1 -60 W] or q ≈ [30 -120 W.m -2 ], correspond typically to measured outdoor radiative deficits R i .

Results

Figure 3a represents a typical evolution of the difference (T d -T a ) and the condensed mass per surface area, µ=m/S c (Kg.h -1 .m -2 ). From µ(t) one deduces the evolution of the condensation rate dµ/dt. A numerical treatment is necessary to smooth out the µ data before differentiating (function "weight" of Kaleidagraph, rate 10%). From these smoothed data is obtained Fig. 3b, where dµ/dt is correlated with T d -T a . A simple linear fit well describes the data:

        négative if positive if T T dt dµ a d 0 0   (10)
The slope  (kg.h -1 .m -2 .K -1 ) is reported on Fig. 4a with respect to q for several experiments corresponding to the range [30 -120 W.m -2 ]. In spite of data scattering, it is seen that the  values are not correlated with q, the mean value being  = (6.1 ± 0.6)10 -3 kg.h -1 .m -2 .K -1 (uncertainties: one SD). The variation of µ 0 (kg.h -1 .m -2 ) with respect to q is drawn in Fig. 4b.

A clear proportionality is found with q:

  0 0 q q     (11)
Here q 0 represents the power threshold to obtain condensation water in the beaker. One finds q 0 = (15 ± 10) Wm -2 and  = (1.3  0.2)10 -3 kg.h-1.W -1 (uncertainties : one SD). This experimental threshold has not to be taken into account in the general relation between µ 0 and q, which can be eventually written as

q    0 (12) with  ≈ 1.310 -3 kg.h -1 .W -1 .  3.3. Discussion
The variation of dµ/dt with T d -T a can be explained as a process that is limited only by heat losses with neighboring air. The effect of heat losses appears then to be more important in dew formation than the effect of vapor pressure difference and mass diffusion, Eq. 5.

Qualitatively, when T d  T a , although the vapor pressure gradient at the surface is low, the heat losses are vanishing. The cooling power is thus nearly uniquely used to condense water by compensating for the latent heat of condensation. The rate of condensation is then maximum, dm/dt = µ 0 . When T d << T a , the power is mostly used to cool the condenser and only little power remains available for condensation, whose rate strongly decreases.

Condensation is cancelled when all the power is used to cool the condenser, corresponding to the maximum temperature difference

     q T          0 0 , ( 13
)
whose amplitude obviously increases with cooling power q.

For a more quantitative approach, let us consider Eqs. 1-7, where R i. = -qS c . In the stationary regime where dT c /dt= 0, it comes for the available condensing power:

  a d c c c T T L a L q dt d dt dm S      1 . ( 14
)
This expression is identical to Eq. 10 where µ 0 = qL c -1 , that is (Eq. 12)

 = L c -1 (15) and c L a   (16)
Let us compare these values with the experimental data. With L c  2500 J.g -1 , one gets = 4 10 -7 kg.J -1 , which compares well with the experimental value 3.610 -7 kg.J -1 . Concerning the temperature dependence, the experimental value 1.310 -3 kg.h -1 .m -2 .K -1 corresponds to a heat transfer coefficient a  1 W.m -2 .K -1 . This value is lower but in the expected range of Eq. 4.

The estimation of a precise value for the heat transfer coefficient would need a thorough study of air flow around the plate, e.g. by CFD (see [START_REF] Clus | Comparison of Various Radiation-cooled Dew Condensers Using Computational Fluid Dynamics[END_REF]. This study is out of the scope of the present paper.

From the above study one thus concludes that dew yield follows simple Eq. 14 with respect to cooling power q and temperature difference (T d -T a ). The heat transfer coefficient a has nevertheless to be determined for each particular condenser and air flow configuration.

Radiative condensers

Similarity and differences with laboratory study

By similarity with the above laboratory case, one now aims to estimate the natural dew yield of an atmospheric radiative condenser by applying Eq. 10 or 14. Cooling heat flux is now ensured by the radiation deficit R i . The emissivity of the surface that is open to sky is assumed to be equal to 1. The shape and size of the condenser as the particular air flow around it will determine the heat transfer coefficient, a. For condenser thermally insulated from below (the surface not open to sky), heat exchange is only due to air convection. The latter is a mix of natural and forced convection, a difficult problem that can only be approached with CFD simulations (see e.g. [START_REF] Clus | Comparison of Various Radiation-cooled Dew Condensers Using Computational Fluid Dynamics[END_REF]). However, one can give general rules when considering the different condenser geometries used so far. One can distinguish [START_REF] Clus | Comparison of Various Radiation-cooled Dew Condensers Using Computational Fluid Dynamics[END_REF]

) (i)
planar condensers, horizontal or inclined (around 30°) and (ii) hollow condensers, such as cones, pyramids. Other shapes are (iii) mixed hollow and planes as egg-box and origami [START_REF] Beysens | New architectural forms to enhance dew collection[END_REF]. For any wind direction and wind speed lower than 4 -5 m. s -1 , the yield of these condensers vary only in a range of  30% (if one excepts the origami shape; due to edge effects, it provides much more efficient dew drop collection at low dew yield). Within this wind speed range, dew yield can thus be expressed within about 30% for any condenser shape with the same heat transfer coefficient, which has to be determined experimentally.

The condensation rates are usually measured in L.m -2 .d -1 = mm.d -1 (L is for litre, d is for day), denoted dh/dt. Measurements are collected in 10 different sites in the world, corresponding to various climates (see Table 1). The T d -T a dependence of dew yield leads to typical dependence where nearly all data lie below a line (see e.g. [START_REF] Lushiku | Optical properties of obliquely evaporated aluminium films[END_REF]; Muselli et al., 2006 and Figs. 5ab). This line, with mean slope on order 0.06 mm.d -1 .K -1 , corresponds to Eqs. 10 and 14 above with a slope close to the experimental value found in the laboratory experiments, section 3 (  0.006 kg.m -2 .h -1 .K -1  0.07 mmd -1 K -1 ). The maximum natural dew yield is on average about 0.37 mm.d -1 , corresponding to a mean maximum cooling temperature difference to obtain dew of about -6°C. The mean line that envelops the data (Figs. 5ab) can thus be considered as the dependence of dew yield on (T d -T a ) in the laboratory experiment (Fig. 3b). It corresponds to the maximum cooling power available at a given site with the considered type of condenser. The yields below this line correspond to lower available powers due to weather conditions: strong winds occurrence (enhances convective heat transfer) and/or presence of clouds (reduces radiative power).

In the following, one estimates the two factors that enter in Eq. 14, cooling power, q, and thermal exchange, a. Some other parameters can enter in the evaluation as e.g. the condensation time, which is related to the different seasons.

Condensation time

In many places in the world weather stations can be found in airports. Data are usually collected on a periodic basis (denoted (dh/dt) t witht in h.). In remote areas measurements are manual and performed only from the sunrise to the sunset. Then only measurements at or just before the sunrise can be obtained. They are denoted by (dh/dt) 1 . As dew forms generally under stable anticyclonic conditions where sky is clear, these measurements can be used were no other data available, however the uncertainty in doing so remains mostly ignored. The calculated dew yield will thus correspond to mean night duration of 12 h. The seasonal variation of the night duration, , can be accounted for by rescaling the data, denoted (dh/dt)  

1 12              dt dh dt dh   . ( 17
)
The time  (h.) can be expressed as a function of the date d counted in day, latitude  of the site from e.g. the following formula: (18) When measurements are performed on a periodical basis with interval t (e.g. t = 1/4 h.), the above correction is not necessary: air temperature rise during the day and the difference in T a -T d becomes too large to provide dew yield data. A correction, however, has to be given; with t in h., one gets:

                        
1 12                dt dh t dt dh t (19)

Cooling power

In absence of solar radiation, the cooling power R i is the difference between the radiative power of the condenser emitted in the infra-red and absorption by the same condenser of the IR emission of the sky. Emissivity of the condenser is assumed above in section 4.1 to be equal to 1 (black body emissivity). As the temperature of the condenser remains close to the atmosphere temperature, the radiative deficit measured by R i is proportional to the difference between the condenser and sky emissivities in the IR atmospheric window (7 -14 µm). This deficit varies linearly with the solid angle of clear sky, classically measured by N, the cloud cover measured in okta. One eventually obtains (with

T c ≈ T d , in °C):   ) 8 1 ( 15 . 273 ) 1 ( 4 N T R d s i       . ( 20
)
Here  (= 5.670 10 -8 W.m -2 . K -4 ) is the Stefan-Boltzmann constant.

Dew can form only within a T a -T d range of 10 K (Fig. 6). Then in many places dew events occur for absolute values of T d ( T a ), denoted by T d (K), which does not vary more than 5-10 % in the year around the mean value T d = 285 K (Fig. 6). A further approximation (not mandatory as seen below, Eq. 25, it just simplifies the calculations) will thus to consider a constant temperature T d in Eq. 20, which becomes:

  ) 8 1 ( 285 ) 1 ( 4 N R s i      (21)
The sky emissivity is a function of the water vapor content of air, a quantity which can be estimated from T d and elevation H of the considered site. One considers for the sky emissivity the formulation by [START_REF] Berger | Clear sky radiation as a function of altitude[END_REF]. With T d in ° C and H in km:

 s =0.2422[1+0.204323H -0.0238893H 2 -(18.0132 -1.04963H + 0.21891H)10 -3 T d ] (22)

Wind influence

The effect of wind couples with natural thermal convection to enhance convective heat transfer. It is expressed by the windspeed influence of coefficient a. In real experiments, the shape of the condenser and obstacles in its proximity can deeply modify air flows. For instance, [START_REF] Clus | Study of dew water collection in humid tropical islands[END_REF] used natural air breakers (coconut forest) to increase the dew yield by a large factor. Practically speaking, it is quite difficult to obtain dew for windspeed V (measured at 10 m elevation) larger than V 0 = 4.4 m/s. One will thus simply consider a cut-off function where the heat exchange increases much above V 0 , as e.g.:

                                     0 0 20 0 0 101 1 exp 1 100 1 ) / ( V V if V V if V V V V C . ( 23
)
The dew yield can then be expressed as

                negative if positive if V V C T T R dt dh a d i 0 / 0 * * 1   ( 24
)
with   and  being adjustable parameters on order the values and  determined in the above laboratory experiments, section 3.

Summary

According to the above discussions, the dew yield dh/dt can be evaluated according to Eqs.

19, 24, where C(V/V 0 ) is given by Eq. 23 and R i by Eqs. 20 or, in a simplified manner, by Eq.

21. The quantities   =4.0810 -3 L.d -1 .W -1 and   = 0.06 mm.d -1 .K -1 are taken from the mean experimental values from natural dew condensation of the sites in Table 1. One eventually obtains the following relationship, where (dh/dt) is in mm.d -1 :

                                                                                   negative if positive if V V T T . -N/ . T T H . H + . - . - H . H - . + .

Evaluation and discussion

Dew yields calculated from Eqs. 19, 25 are compared with measurements performed in 10 different sites (Table 1), using either 1m 2 , 30° tilted condensers or 0.16 m 2 horizontal planar condensers. There are two exceptions, the use of a 8m 2 , 30° tilted roof slope in Kothara (India) and a 0.32 m 2 horizontal planar condenser in Bordeaux (France). There were no corrections made for these different configurations; the same formula Eqs. 19, 25 were used.

As discussed above in section 4.1., the value of the heat transfer coefficient does not vary much, experimentally speaking, for these planar condensers. As a matter of fact, in Figs. 78below, no obvious systematic variations between the different types of condensers can be observed. The natural variations due to the precise characteristics of air flow due to the particularities of the condenser location is larger than the approximation made.

The comparison between experimental and calculated values is performed by the quality of the correlation between the cumulated sum of experimental and calculated dew yields from

day d 1 to day d 2 , sum               2 1 exp d d dt dh dt dh and sum  , 1 2 1              d d calc dt dh dt dh
, respectively (Fig. 7). The sum is indeed the quantity of interest and has the merit to smooth down the daily uncertainties. A linear fit is then performed,

sum exp       dt dh = Y. sum calc dt dh       (26)
from which the proportionality factor Y , expected unity, is deduced. The Y values for the 10 investigated sites are reported in Table 1 and Fig. 8, with the mean value 0.95  0.05 (one SD). The value obtained at Grenoble has been discarded in the fit because this site is located in an urban valley where radiative cooling is lowered by anomalously low atmospheric transmittance. When looking at Fig. 8, one sees that the experimental values are lower or equal than the calculated values. This is expected as the local air flows and IR radiation can only increase heat losses and thus lower cooling. In addition, dew water collection is sometimes measured without scraping, which also lowers the collected volume (a typical value for scraped volume is 0.04 mm, see [START_REF] Muselli | Dew water collector for potable water in Ajaccio (Corsica Island, France)[END_REF]. There are no obvious correlations of the magnitude of the differences with the climate zones.

Conclusion

From laboratory test experiments on a planar surface a general linear relationship is derived between dew yield and cooling power and difference in dew point and air temperatures. This relationship implicitly demonstrates that dew yield is mainly limited by convective heat losses. It is generalized to natural dew condensation by radiative cooling on a planar surface with emissivity unity.

Limitations of the model are concerned with its intrinsic limited precision (it does account for precise radiative and heat transfer data) and the fact that meteo data are not always available close to the place where dew are needed. In particular, possible deviations may stem from differences in altitude between the place where meteo data are collected and the site under examination [START_REF] Kidron | Altitude dependent dew and fog in the Negev Desert, Israel[END_REF] .

In

Tables and Tables Captions

Table 1. Characteristics of the investigated sites and collected data. a :

Figures and Figures captions

  be made unity for most locations.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Indoor experimental setup. During measurements the window is left half open and only one thermocouple is used. (For notations, see text).

Fig. 3 .

 3 Fig. 3. (a) Typical evolution of the condensed mass per surface area (µ, left ordinate) and of the temperature difference T d -T a (left ordinate) (P = 6.3 W or q = 77 Wm -2 , 4 days). (b) Rate of condensation dµ/dt (Kg.h -1 .m -2 ) from the (a) data with respect to T d -T a . The line is a linear fit (Eq. 10).

Fig. 4 .Fig. 5 .Fig. 7 .Fig. 8 .

 4578 Fig. 4. Variation with cooling power q of (a) slope  and (b) maximum rate µ 0 (see Eq. 11).The hatched area is not experimentally accessible.

  the model formulation, only a limited number of regular and commonly available meteorological variables are needed: cloud cover, windspeed, air and dew point temperature, site elevation. This dew yield evaluation is compared with experimental data obtained in 10 different sites in the world showing different climates. A good agreement between calculated and collected values is found, in spite of the simplifications being made in the model. It is thus anticipated that such simple expression can be useful to model dew formation in numerous places in the world and eventually give general maps of dew potential. Such maps include the potential use of dew by plants.

	Glossary
	Latin symbols	Units		Definition
	a		W.K -1 m -2	convective heat transfer coefficient
	b		W.m 2		relation heat flux-electric power fitting parameter
	c	Greek symbols	W	Unit	relation heat flux-electric power fitting parameter Definition
	C(V/V 0 ) c c    c a ,   c w  a d  D T g  a  s k µ L µ 0 L c  M  m 	W J.Kg -1 . K -1 kg.h -1 .m -2 .K -1 kg.h-1.W -1 J.Kg -1 . K -1 J.Kg -1 . K -1 K -1 d. deg. m 2 .s -1 m.s -2 W.m -1 .K -1 W.m -1 .K -1 Kg.h -1 .m -2 m Kg.h -1 .m -2 J.Kg -1 m 2 .s -1 Kg W.m -2 . K -4 Kg h.	cut-off function condensation rate -temperature correlation parameter specific heat of condenser material condensation rate -temperature correlation parameter specific heat of air air thermal expansion specific heat of water latitude time air thermal diffusivity air thermal conductivity stainless steel thermal conductivity earth acceleration constant condensed mass per surface area corrective factor to convective heat transfer coefficient a condensation rate -temperature correlation parameter plane sheet length air dynamic viscosity condensation latent heat Stefan-Boltzmann constant condenser mass condensate mass condensation time
	N		okta		cloud coverage
	Nu			Nusselt number
	P		W		electric power
	p 0	Pa		atmospheric pressure
	P 0	W		power threshold
	p a (T a )	Pa		air water pressure
	p sat (T)	Pa		saturation water vapor pressure at temperature T
	q		W.m -2		cooling power per unit surface
	q 0	Wm -2		power threshold
	Ra			Rayleigh number
	R cond	W		condensation energy per mass unit
	RH	%		relative humidity
	R he	W		heat exchange with ambient air
	R i		W		cooling energy
	S c		m 2		condenser surface
	t		s		time
	t	h.		measurement period
	T a	°C or K		air temperature
	S c		m 2		condenser surface
	T c	°C or K	condenser surface temperature
	T d	°C or K		dew point temperature
	f		W.K -1 .m -2 .s 1/2	heat transfer coefficient factor
	T p	°C or K		Peltier element temperature
	V		m.s -1		air or wind speed (measured at 10 m elevation, unless specified)
	V 0	m.s -1		cut-off wind speed
	Y				proportionality factor

Acknowledgments

Critical reading, comments and corrections of the manuscript by V. Nikolayev and M. Tomaszkiewicz are thankfully acknowledged. O. Clus, A. Dejoan, R. Lee, I. Lekouch, M. Mileta, I. Milimouk-Melnytchuk, M. Muselli, G. Sharan are gratefully thanked for their contribution in the data collection.