C Seceh

C Pinazo

M Rodier

K Lajaunie-Salla

C Mazoyer

C Grenz

R Le Gendre

Biogeochemical model of nitrogen cycling in Ahe (French Polynesia), a South Pacific 1 coral atoll with pearl farming 2

Keywords: Biogeochemical model, Ahe atoll, pearl farming, phytoplankton, nitrogen cycle 22

A biogeochemical model (ECO3M-Atoll) was configured to simulate the lower food web in 10 Ahe Atoll lagoon where phytoplankton is mostly nitrogen limited. Understanding the 11 dynamics of phytoplanktonthe main food source for oystersis crucial for the management 12 and the allocation of new pearl farming sites. After parametrizing the model with in situ 13 observations, we tested different hypotheses about nitrogen cycling (benthic remineralization, 14 atmospheric N fixation, etc.) and compared the results to a large observational dataset. Model 15 results show that simulated (pico-and nano-) phytoplankton biomass and nitrogen 16 concentrations are close to in situ data. The simulated biogeochemical processes (uptake and 17 primary production) are also very similar to the observed values. In the model, primary 18 production ranged from 1.00 to 2.00 mg C m -3 h -1 for pico-and 0.40 to 1.00 mg C m -3 h -1 for 19 nanophytoplankton; mean N uptake was 2.02 µmol N m -3 h -1 for pico-and 1.25 µmol N m -3 h - 20 1 for nanophytoplankton. 21

Introduction 23

After tourism, pearl farming represents the second largest source of income in French-

24

Polynesia. The country dominated the market for black pearls during the 1980-90's. However, 25 since the early 2000s, the sector is in crisis (Andréfouët et al., 2012), further exacerbated by 26 the complexity of pearl farming. Pearl production depends on the life cycle of Pinctada margaritiferathe black-lip pearl oysterand the success rate of farming is only about 30 % 28 (about 300 sellable pearls per 1.000 grafted oysters) (Andréfouët et al., 2012).

29

In French Polynesia, pearl oysters are reared in fairly deep atoll lagoons. Atolls can be 30 defined as productive micro-environments within an otherwise oligotrophic ocean. Indeed, 31 atoll lagoons typically exhibit higher phytoplankton biomass and production compared to the Ahe Atoll is located in the north-western part of the Tuamotu Archipelago in French 97 Polynesia, about 500 km north-east of Tahiti ( 98 Fig. 1). Ahe is a semi-enclosed atoll with a lagoon that is connected to the open ocean by

Dataset 118

For a multi-year model-data comparison, we used a large dataset consisting of data from and nanophytoplankton were measured at each station ( 13 C/ 15 N method). At L0, we also 143 obtained vertical profiles of primary production from the surface to a depth of 40m, at 5m The model describes both the carbon and nitrogen cycles and consists of six 165 compartments that use either carbon or nitrogen units: picophytoplankton (pico-), 166 nanophytoplankton (nano-), bacteria, detritic particulate organic matter (DPOM), and labile 167 dissolved organic matter (LDOM). At Ahe, phytoplankton are not limited by phosphorus 168 (Charpy et al., 2012). The DOM compartment contains ammonium (NH4), nitrate + nitrite 169 (NOx), and dissolved oxygen (O2). In total there are 15 state variables (Table 1), and even 170 chlorophyll a, which is a diagnostic variable, is also calculated from the phytoplankton's 171 internal N/C ratio 𝑄 𝐶 𝑁 𝑝ℎ𝑦𝑡𝑜 (Faure et al., 2006(Faure et al., , 2010a;;Smith and Tett, 2000) (see Appendix

172

A). Moreover, this internal N/C ratio varies between prescribed phytoplankton-specific upper 173 and lower bounds and is recalculated at each time step. This ratio contains information about 174 the nutritional state of the cells when compared to the Redfield ratio (Redfield et al., 1963).

175

This nutritional state is taken into account to calculate the growth and nutrient uptake rates 176 (Tett, 1987). The same framework is used to express bacterial processes (Thingstad, 1987). The model was forced using realistic average temperatures, wind velocities , and light )) ( 4)

213
where PARmax is the maximum value of PAR (in µmol photons s -1 ) at noon and t is time (in Willmott index (d1) [START_REF] Willmott | Some Comments on the Evaluation of Model Performance[END_REF] are calculated using:

218 𝑀𝐴𝐸 = ∑ |𝑀 𝑖 -𝐷 𝑖 | 𝑛 𝑖=1 𝑛 (5) 219 𝑅𝑀𝑆𝐸 = √ ∑ (𝑀 𝑖 -𝐷 𝑖 ) 𝑛 𝑖=1 2 𝑛 (6) 220 𝑃𝐵(%) = ∑ (𝐷 𝑖 -𝑀 𝑖 ) 𝑛 𝑖=1 ∑ 𝐷 𝑖 𝑛 𝑖=1
× 100 (7) 3) where the continuous PAR measurements were performed.

221 𝑑1 = 1 - ∑ (𝑀 𝑖 -𝐷 𝑖 ) 2 𝑛 𝑖=1 ∑ ((𝑀 𝑖 -𝐷)+(𝐷 𝑖 -𝐷)) 2 𝑛 𝑖=1 (8)

228

To assess the model sensitivity to external forcing, the light and temperature ranges were PARmax and the water temperature were increased in 10 steps from 100 to 1300 µmol 287 photons m -2 s -1 and 23 to 31 °C, respectively. We then compared the final pico-and nano-

288

biomasses obtained for these different forcing levels (Fig. 4).

289

Pico-is more sensitive to changes in environmental forcing than nano-. Indeed, pico-290 varies between 0 and 0.2 µg Chla.L -1 , while nano-varies between 0 and 0.125 µg Chla L -1 .

291

Moreover, below about 250 to 400 µmol photons m 2 s -1 , the impact of temperature changes 292 are rather small on phytoplankton biomass, resulting in a pico-biomass of 0.0 and 0.10 and 293 nano-biomass of 0 and 0.075 µg Chla L -1 for temperatures of 31°C and 25°C, respectively.

294

For higher light intensities, primary production is no longer light-limited and becomes more 295 sensitive to temperature. For example, at 700 µmol photons m 2 s -1 , the pico-biomass is 1.6 296 times higher and the nano-biomass increased by a factor 2.

297

For the light and temperature ranges observed during the AHE2017 campaign, i.e., 298 temperatures between 28.3 and 29.5°C and PAR between 550 and 1200 µmol photons m 2 s -1 , 299 the model predicts only very small changes in phytoplankton biomass (white box in Fig. 4). 300

Sensitivity to model parameters

303

Indices of sensitivity (IS) for phytoplankton chlorophyll a, nutrients, and dissolved and 304 particulate organic nitrogen are presented for a ± 10 % variation in parameter values (Fig. 5).

305

The fractions of dissolved organic carbon (dC) and nitrogen (dN) assimilated by zooplankton 306 were found to be the most sensitive parameters and influence all the state variables shown in Ahe lagoon (Charpy et al., 2012). Results of primary production (Fig. 6.A) show a clear 330 spatial pattern with maxima of about 2 mg C m -3 h -1 for pico-and 1 mg C m -3 h -1 for nano-at 331 Station L1, which seems to be about 2 to 3 times more productive than other stations. At all 332 stations, nano-contributed between 25 and 40% to the total primary production, with a 333 lagoon-wide average of 32%. Moreover, the three southern stations (L0, L1 and L8) seem to 334 show a higher proportion of PP by nano-compared to the two northern stations.

335

NH4 and NOx uptake rates from the model and in situ observations cannot be compared 336 quantitatively because of the difference between nutrient limitation during the experiments 337 and in the model. . However, we can compare the ratios between pico-and nano-and between

338

NH4 and NOx uptake rates at different stations. Everywhere, uptake of NH4 was greater than 339 of NOx (Fig. 6.B.). Moreover, uptake rates were greater at L1 and lower at L4. The NH4 340 uptake by pico-represented more than 50% of the total NH4 uptake, except at L1 and L8. At 341 all stations except L1, NOx uptake appears lower than NH4 uptake. The NOx uptake by pico-342 at L1 and L8 represent 70% of the total and more than 80% at L0, L4, and L10. At each station and for each grazing scenario, the pico-biomass was lower than in S0 358 even if the nano-grazing rate was increased (Fig. 7). In contrast, the nano-biomass was lower 359 when the nano-or both the pico-and nano-grazing rates were increased (S1.3). At all 360 stations, the S1 and S0 nano-biomasses are nearly identical. At L1 and L4, the S1.1 and S1.3 NOx concentrations were higher than in S0, increasing from about 0.012 to 0.035 µmol L -1 for 365 NH4 and 0.10 to 0.18 µmol L -1 for NOx, when the grazing rates are increased. This increase is 366 more pronounced when just the nano-or both the pico-+ nano-grazing rates are increased. In 4). These benthic fluxes 383 varied between stations with higher values observed at L1 and L8 (Grenz et al., this issue). In

392

In the nitrogen fixation simulation (S3), all variables were higher than in situ values. N 393 fixation had no effect on NH4 concentration but led to high NOx concentrations at L4, L8, and 394 L10. Moreover, the simulation results were improved with regard to the pico-biomass at L1.

395

Compared to S3, the S4 simulation, which considers anthropogenic inputs of NOx, led to an 396 even higher increase in concentrations at all stations, except for nano-. Moreover, the S4 pico-

99

  just one active pass on the north-western side of the atoll rim. Moreover, several hoa (shallow 100 reef flat spillways) exist on the southern and north-western sides of the rim. The lagoon 101 covers an area of 142 km 2 (main length = 23 km), has an average depth of 41 m (maximum 70 102 m), and a renewal time of about 250 days (Dumas et al., 2012). The climate is wet tropical 103 with one rainy season from November to April. Maximum precipitation occurs in December 104 and January. The air temperature varies only slightly over a year (25 -29 °C). The wind 105 regime is dominated by moderate trade winds blowing from East-South-East (60° to 160°) 106 and with strong southerly winds in the austral winter (Dutheil et al., 2020). Our study period 107 (November/December 2017) corresponds to the hot season at the beginning of the rainy 108 period. Weather data indicated that while the rainy season had not yet started in November 109 2017, temperatures had already risen significantly since October 2017. During our field 110 campaign, we only had one rain event (December 2, 2017) and a constant trade wind regime 111 throughout.

Fig. 1 .

 1 Fig. 1. Left: Location map of French Polynesia and Ahe Atoll. Right: Locations of sampling115

  116

  117

  144 intervals. The resulting P/I curve was used to calibrate the relationship between solar 145 irradiance and photosynthesis in the model. Daily primary production was calculated from 146 carbon fixation and a photoperiod of 11.5h. 147 Finally, benthic flux chambers were deployed at each station to quantify nutrients (NH4, NOx, Si(OH)4, PO4) and oxygen fluxes at the sediment-water interface. Two different kinds of 149 chambers were used: one opaque chamber to simulate nighttime and a transparent chamber to 150 expose the sediments to the ambient light regime. More details can be found in Grenz et al. 151 (this issue).

163 Fig. 2 .

 1632 Fig. 2. Schematic diagram of the biogeochemical cycles represented in the ECO3M-Atoll model showing all state variables, processes, and forcings.

207PAR

  intensities in order to reproduce the ecosystem functioning at 3m depth. All stations used the 208 same constant temperature and wind speeds of 28.4 °C and 5.4 m s -1 , respectively, 209 corresponding to the mean in situ values during the AHE2017 campaign. Wind was used only 210 to drive oxygen aeration and light was prescribed based on a day/night cycle using actual 211

215

  Different metrics are used for the statistical model-data comparison. The mean absolute 216 error (MAE), the root mean square error (RMSE), the percentage model bias (PB), and the 217

  model sensitivity to environmental forcing and parameters were 227 performed at station L0 (Table

229

  chosen to be representative of the typical values encountered in Ahe atoll. The light range is 230 based on PARmax (see Section 2.2). The temperature range was chosen based on a one-year 231 in situ dataset (Sangare, pers. comm.).

  was performed using the index described by Chapelle et al., p is the percentage of parameter change (± 10 % in this study), N = 3600 (only the last 237 150 days are taken into account with hourly results), Xi is the variable value at time t after the 238 parameter change, Xi raw is the variable value at time t in the control simulation. IS% is used to 239 identify the most sensitive parameters (i.e., parameters whose variation causes the strongest 240 deviation of state variables from the reference simulation).

  cycle components were tested. In simulation S2, we added in situ benthic fluxes 268 obtained in 2017 using benthic chambers. Benthic nitrate and ammonium fluxes were 269 implemented as follows: the fluxes measured in dark chambers were used during night-time 270 and those measured in transparent chambers during the day were used during daytime (

307Fig. 5 .Fig. 4 .Fig. 5 .

 545 Fig. 5. These parameters represent the ratio of the dissolved over the particulate pool, once 308

  344

Fig. 6 .

 6 Fig. 6. Maps of modeled biogeochemical fluxes at all 5 stations. A: Primary production (PP) 345

  361nano-biomasses we are very similar. Overall, the simulated pico-biomass appears to be 362 closer to in situ values at L4 and L8. Comparing between different simulations, the nano-363 biomass appears closer to in situ values in S1.1 and S1.3. In all grazing simulations, NH4 and 364

367 371 Fig. 7 .

 3717 Fig. 7. Comparison between in situ data and the SO and S1.1-3 model outputs at four stations.372

  at the sediment -water interface show some differences between 379 NH4 and NOx fluxes (Grenz et al., this issue). NH4 fluxes were always positive (i.e., from 380 sediment to water column) except at L10 where they were negative during the day. In 381 contrast, NOx fluxes were always positive during nighttime and always negative during 382 daytime. Moreover, NH4 fluxes were lower than NOx fluxes (Table

  384 the S2 simulation (benthic fluxes simulation), NOx concentrations at L1 and L10 decreased 385 significantly (by about 0.1 µmol L -1 ), while at other stations this decrease was less 386 pronounced (about 0.05 µmol L -1 ). Modeled LDON was also lower at all stations. Concerning 387 NH4, no variation of concentrations is observed. Benthic fluxes reduced ambient NOx 388 concentrations. These NOx concentrations are lower than in situ data at all stations, except at 389 L1 where they are within the standard deviation. Overall, the modeled phytoplankton biomass 390 was lower at each station, with the simulated nano-biomass closer to in situ values at all 391 stations except L4.

Fig. 8 .

 8 Fig. 8. Comparison between in situ data and model outputs. Reminder: S0 -Control, S2benthic flux forcing, S3 -N fixation, and S4 -NOx supply. Black vertical bars represent one standard deviation and black horizontal bars represent in situ means. Note that LDON values have been divided by 30 to fit the scale of this figure.

  on forcing conditions suggested us to set the same light and 403 temperature on all stations. We observed no significant changes in the pico-or nano-404 biomasses when varying the forcing conditions within the ranges observed during the 405 AHE2017 field campaign. We therefore applied the same constant environmental forcing 406 (water temperature of 28.5°C and PARmax of 800 µmol photons m -2 s -1 ) across the model 407 domain. Moreover, this analysis confirms that the model conveys the lack of photo-inhibition 408 measured in the Ahe lagoon(Lefebvre et al., 2012). This is partly due to the shape of the 409 primary production equation and, more specifically, how it accounts for light limitation (see phytoplankton grazed but also indirectly affects NH4 via the remineralization through the 434 were based on specific in situ measurements of nutrients and 438 phytoplankton concentrations as well as biogeochemical processes(Rodier et al., 2021). Some 439 of the model results presented in Section 3.3were close to in situ data. The model predicted proximity to a local village (which may add anthropogenic inputs) and to high-density pearl 450 farms(Andréfouët et al., 2012). In contrast, L4 has the lowest residence time as it is near the 451 pass and thus exposed to more oligotrophic oceanic water(Dumas et al., 2012). These spatial 452 differences are also visible in the in situ data(Rodier et al., 2021). Nevertheless, since the 453 model is 0D, the inflow of oceanic water through the pass is not accounted for and the above 454 explanations cannot be used to explain the differences observed in the model results which 455 must therefore be due to differences in the initial conditions. 456 Moreover, in the reference simulation, NH4 uptake by nano-represented less than 50 % of 457 the total, except at L1 and L8. The same results were found in situ by Rodier et al. (2021) for 458 L1, where nano-uptake reached 57% of the total, but not at L8. This may be again due to the 459 fact that L1 is located near high-density pearl farms (Andréfouët et al., 2012), hence nano-, 460 which is more grazed by oysters, may have adapted to the higher grazing pressure by 461 increasing their NH4 uptake rates. L8 is not well represented by the model which may also be 462 due to its particular location at the confluence of the two main circulation cells (Dumas et al., 463 2012). This station is thus influenced by both, oceanic water entering through the pass and 464 nutrient rich water coming from the SW part of the lagoon. As the model does not account for 465 any horizontal transport, it cannot represent this phenomenon correctly. The present resultsthus merely reflect of our choice of initial conditions. At all stations, NOx uptake was lower 467 than NH4 uptake, in both in situ data and the model results. In the model, L1 showed the 468 highest NOx uptake while in situ the uptake was highest at L0. Our choice of the initial 469 phytoplankton biomass at L0 may have been too low compared to in situ data. Concerning the 470 ratio of NOx uptake between pico-and nano-, measurements showed clear spatial differences 471 across the lagoon, with 37 % of total NOx uptake by nano-at L1 and > 50 % in the other 472 parts of the lagoon. In the model, on the contrary, the NOx uptake due to picophytoplankton is 473 elsewhere greater than those due to nanophytoplankton at all the stations. may vary depending on the type of predator. As expected, in 477 the model, a higher grazing rate led to a decrease in phytoplankton biomass and an increase of 478 nutrient concentrations. However, pico-was sensitive to changes in grazing on nano-, while 479 nano-was not sensitive to changes in grazing on pico-. In addition, while NH4 seemed rather 480 sensitive to changes in grazing it was relatively unaffected by other parameter changes 481 (simulations S2-4). In contrast, NOx was less affected by changes in grazing pressure and 482 more sensitive to changes in the other parameters. In the grazing simulations (S1.x), the nano-483 biomass values were closer to the in situ ranges which confirms that nano-would be 484 preferentially grazed by oysters and other higher predators. Moreover, modeled NH4 485 concentrations in the grazing and benthic fluxes simulations (S2) were closer to in situ 486 values. The model thus seems to confirm that part of the remineralization described in Ahe by 487 Lacoste and Gaertner-Mazouni (2016

517

  ability of the model to represent the impact of remineralization by the grazing in water 518 column and the sediment. Finally, nitrogen fixation and NOx inputs allowed to increase the 519 low NOx concentrations.520One of the limitations in our approach was that we set the same light and temperature 521 conditions at all five stations. We did this because the sensitivity analysis did not show any 522 significant variability in phytoplankton biomass for the range of PAR and temperature values 523 observed during the AHE2017 field campaign. Nevertheless, in situ data showed small spatial 524 variabilities in temperature and phytoplankton community composition between the SW and 525 the other areas of Ahe lagoon. This could not be reproduced by our model. However, the 526 observed variation in phytoplankton communities may be caused by various factors such as 527 the presence of other organisms, nutrient conditions, pearl farms, anthropic inputs, etc.528Moreover, the dC and dN parameters were much more sensitive than in the ECO3M-Lagoon 529 configuration on which our ECO3M-Atoll model is based. This may be due to respiration 530 being constant and the fact that we used two instead of one phytoplankton compartment. In 531 the future, respiration could be controlled via a similar quota-based function that already 532 controls nutrient uptake and growth.533The model was run in 0D, which means that the forcing was constant and the 534 hydrodynamics (circulation, stratification, vertical mixing, etc.) were not represented. In the 535 future, ECO3M-Atoll will be coupled with a hydrodynamic model (MARS3D) will introduce 536 some more realism and variability to the modelled processes to facilitate a more in-depth 537 understanding of how the hydrodynamics and different temperatures and irradiances may 538 influence the biogeochemistry at Ahe Atoll. Moreover, by upgrading the model to 3D, the 539 forcing (grazing by oysters, benthic fluxes, anthropogenic inputs, N fixation) can vary 540 spatially and as a function of depth. Finally, the coupled model should be able to provide 541 information regarding the trophic forcing to the oyster dynamic energy budget (DEB) model 542 by Thomas et al. (2012) (see also Sangare et al., 2019). This set of coupled models will help 543 to investigate the influence of biogeochemistry on the life cycle of pearl oysters and on the 544 farming activity.545 546 To conclude, this study presented the ECO3M-Atoll model, a new biogeochemical model 547 specifically configured for Ahe Atoll to study the nitrogen cycle and biogeochemical 548 ecosystem functional in a pearl farming atoll. A better understanding of the local nitrogen 549 cycle is pivotal to understand local phytoplankton dynamics, the principal food item of pearl 550 oysters in deep and semi-closed atolls. Future implementations of the physical-551 biogeochemical-DEB coupled model will contribute to the improved management of pearl 552 farms, not only at Ahe but also at other pearl farming atolls of the Tuamotu Archipelago that 553 show a similar geomorphology to Ahe Atoll.554 555

Table 2 .

 2 Parameters values for pico-and nanophytoplankton used during the calibration

	179
	Variables	Definitions	Units
	Cpico	Picophytoplankton carbon	µmol L -1
	Cnano	Nanophytoplankton carbon	µmol L -1
	Npico	Picophytoplankton nitrogen	µmol L -1
	Nnano	Nanophytoplankton nitrogen	µmol L -1
	Chlapico	Picophytoplankton chlorophyll a	µg Chla L -1
	Chlanano	Nanophytoplankton chlorophyll a	µg Chla L -1
	Cba	Bacteria carbon	µmol L -1
	Nba	Bacteria nitrogen	µmol L -1
	DPOC	Detrital particulate organic carbon	µmol L -1
	DPON	Detrital particulate organic nitrogen	µmol L -1
	LDOC	Labile dissolved organic carbon	µmol L -1
	LDON	Labile dissolved organic nitrogen	µmol L -1
	NH4	Ammonium	µmol L -1
	NOx	Nitrates	µmol L -1

177 Table 1. State variables used in the ECO3M-Atoll model (except Chla which is a diagnostic 178 variable).

191 𝜇 𝑚𝑎𝑥 (𝑇) 𝑝ℎ𝑦𝑡𝑜 = 𝑎 𝑝ℎ𝑦𝑡𝑜 ⋅ exp (𝑏 𝑝ℎ𝑦𝑡𝑜 𝑇) ⋅ 𝑄 𝑝ℎ𝑦𝑡𝑜 (2) 206

Table 3 .

 3 Initial conditions for the five Ahe stations.

	243
			L0	L1	L4	L8	L10
		Cpico (µmol.L -1 )	0.709	0.710	0.347	0.276	0.379
		Npico (µmol.L -1 )	0.029	0.108	0.053	0.042	0.058
		Chlapico (µg Chla.L -1 )	0.259	0.238	0.116	0.093	0.127
		Cnano (µmol.L -1 )	0.187	0.196	0.066	0.049	0.066
		Nnano (µmol.L -1 )	0.029	0.030	0.010	0.007	0.010
		Chlanano (µg Chla.L -1 )	0.069	0.081	0.027	0.020	0.027
		Cba (µmol.L -1 )	0.83	0.83	0.83	0.83	0.83
		Nba (µmol.L -1 )	0.14	0.14	0.14	0.14	0.14
		DPOC (µmol.L -1 )	3.98	16.67	2.50	12.50	12.50
		DPON (µmol.L -1 )	1.25	2.143	0.71	1.79	1.43
		LDOC (µmol.L -1 )	7.50	10.80	9.57	8.76	8.76
		LDON (µmol.L -1 )	2.40	2.65	2.18	1.95	2.16
		NH4 (µmol.L -1 )	0.012	0.013	0.028	0.012	0.025
		NOx (µmol.L -1 )	0.187	0.085	0.073	0.058	0.091
		O (µmol.L -1 )	190	186.5	186.8	181.9	184.1
	244
	245	After this initial sensitivity analyses, two types of simulations were run: a reference
	246	simulation (control) -testing the sensitivity to initial conditions -and simulations to test
		various hypotheses about N inputs and grazing. The initial conditions of state variables were

247

set according to in situ the values at each station (Table

3

). 248 2.4.3.

Sensitivity to initial conditions at the five stations

	256
	257	2.4.4. Sensitivity to grazing mortality
	258	Lacoste and Gaertner-Mazouni (2016) showed that nitrogen remineralization due to the
	259	grazing by oysters (and associated epibiont filter-feeders) was stronger than nitrogen
	260	remineralization in the sediment. Therefore, we ran several grazing simulations (S1.1, S1.2,
		S1.3). Grazing rates were taken from the report of Projet 9ème FED Professionnalisation et

249

Reference simulations (named S0) were run at all stations (L0 to L10) with the same 250 parametrization but different initial conditions. These simulations allowed us to compare 251 modelled fluxes (nutrients uptake rates and primary production), final nutrient concentrations, 252 and phytoplankton biomass to in situ values at each station. 253 Four other simulations testing the process hypotheses were performed at all stations to 254 study the model response to changes in grazing, benthic fluxes, N fixation, and NOx inputs.

255

The influence of two different kinds of nitrogen sources were tested. 261 perennisation de la perliculture (2010). In S1.1, the grazing value for nanophytoplankton was 262 increased from 1.45 to 2.50 d -1 to account for grazing by mesoplankton, oysters, and other 263 higher predators. In S1.2, picoplankton grazing was increased from 1.70 to 1.85 d -1 to account 264 for grazing by nano-and mesoplankton. In S1.3, the grazing rate in both phytoplankton 265 compartments was increased.

Table 271

 271

	277
	278

4). Moreover, as demonstrated by

Charpy-Roubaud et al. (2001)

at Tikehau Atoll, benthic 272 nitrogen fixation may take place in the sediment. Therefore, in simulation S3 simulation we 273 applied a NH4 influx of 0.18 µmol L -1 h -1 . In simulation S4, an exogenous input of 0.36 µmol 274 L -1 h -1 of NOx was used. We measured high NOx values in rainwater (49 µmol L -1 ) and in the 275 ground water below a motu (a coral sand island on the reef crown of an atoll) north of Ahe 276 Atoll (38 µmol L -1 ).

Table 4 .

 4 Benthic fluxes in the model in µmol m -2 h -1 . Positive values represent fluxes from

	279
	280	the sediment to the water column and negative values represent fluxes from the water column
	281	to the sediment.
		NH4		NOx
		Day	Night	Day	Night

285 3.1.

Sensitivity to environmental forcing 286

Table 5 )

 5 . Bias can be considered poor when its value is above 40 % 348(Maréchal, 2004). Pico-and NOD have the lowest bias. Uptake rates of NH4 and NOx show a 349 good result for d1 with significant values for PP, pico-, nano-, NH4 and NOx.

350

Table 5 .

 5 Statistical analyses comparing observations with model results of the S0 simulation.

	351
	352	MAE = Mean Absolute Error, RMSE = Root-Mean-Square Error, d1 = Willmott index
	353	(1982). Note that the row "Uptake NH4 and NO3" represents the ratio between the pico-and
	354	nano-uptake. * Significant values of d1 (> 0.70).
			MAE	RMSE	Bias (%)	d1
		PP	0.40	0.94	61.70	0.77*
		Uptake NH4 NO3	0.27	0.12	43.02	0.10
		Pico-	0.028	0.004	12.22	0.66
		Nano-	0.972	0.258	317.82	0.14
		NH4	0.036	0.070	74.05	0.48
		NOx	0.091	0.171	49.26	0.21
		NOD	2.715	0.920	22.52	0.26

355

A graphical comparison is shown in Fig.

7

and Fig.

8. 356 3.4. Sensitivity to grazing 357

  an increase in NOx. While data on N2 fixation was available for Tikehau Atoll 501 there were no data for Ahe. The high values of NOx measured in the rain water and ground 502 water lens could be due to human activities on the motu or to the local avifauna(Otero et al.,

	503
	504	2018). The improvement representation of NOx concentration in simulations S3 and S4
	505	confirms that additional NOx inputs are indeed quite likely. Other hypotheses can also explain
	506	this high NOx concentrations, namely upwelling generated by an overturning circulation cell
	507	in the north-eastern part of the lagoon (Dumas et al., 2012).
	508
	509	4.4. Conclusions and future work
	510	While many hypotheses have been made to explain the nitrogen cycle and specifically the
		origin of nitrogen in Polynesian atolls, it is still not completely understood. Modelling
	490
	491	near farms. The S2 simulation seems to confirm that remineralization occurs in sediments and
	492	represents about 4 % of the phytoplankton NH4 uptake, which is consistent with the
	493	percentage measured by Rodier et al. (2021).
	494	Except at L1 station where initial NOx concentrations were high, the modeled NOx
	495	concentrations in S0 were lower than in situ data in. To increase these low concentrations, we
	496	tested different hypotheses. First, Charpy-Roubaud et al. (2001) showed that atmospheric N2
		fixation was a potential source of nitrogen input to lagoons. By adding this source, we could

).

Gaertner-Mazouni et al. (2012)

concluded that benthic 488 fluxes may contribute to meet phytoplankton nitrogen requirements near oyster farms. Grenz 489 et al. (this issue) also observed noticeable exchanges between the sediment and water column 497 increase the NOx concentration in the model. N2 fixation may enrich the water column with 498 NH4 after remineralization. Subsequent nitrification can then transform ammonium to nitrates. 499 This nitrification was boosted in the model, which is why, by implementing N2 fixation, the model showed 511 provides a useful tool to quickly test these hypotheses. In this study, we used the new 512 ECO3M-Atoll model to run a set of simulations to test some of these hypotheses in the Ahe 513 lagoon. Overall, the model results were is similar ranges than the in situ data. The 514 simulations improved our understanding of the biogeochemical functioning of Ahe Atoll.

515

More specifically, we could confirm that nano-are grazed by oysters and higher predators 516

(Dupuy et al., 2009)

. Simulations to test the impacts of grazing and benthic fluxes showed the

2.1. Study site

Acknowledgments

556

Appendix A.1.2). The lagoon typically exhibits higher temperatures in its south-western part 411 (Dumas et al., 2012;Rodier et al., 2021). While this higher temperature may affect 412 phytoplankton communities and the overall biogeochemistry, it is not taken into account by 413 our present model. In the future, by implementing different PAR and temperature values at 414 different locations, the model may be able to account better for these spatial heterogeneities.

415

The sensitivity analysis allowed us to understand the behavior of the new model biomass. In summary, our analysis confirmed that that changes in grazing mostly affect 432 phytoplankton and ammonium as grazing not only has a direct impact on the amount of the share of nano-in the total primary production in the lagoon to be 32 % while in situ data 441 suggests a contribution of 25 ± 12 %. There was a clear difference between the northern and 442 southern parts of the lagoon: while nano-contributes only about 25 % of total primary 443 production at the northern L4 and L10 stations, in the south at L0, L1, and L8 it is of the order 444 of 40 % (Fig. 6A). In the in situ data, there appears to be more of an east-west rather than 445 north-south divide (Rodier et al., 2021).

446

Modelled uptake rates of both NH4 and NOx were highest at L1 and lowest at L4 (Fig.


Keywords: ElectroMagnetic Pulse, Fault Injection, Inductive Probe

ElectroMagnetic Fault Injection requires two main devices, a pulse generator and an electromagnetic (EM) injection probe. To improve security characterizations, inductive probes need to be optimized as regards the pulse waveform and field distribution. The improvement of these parameters leads to greater electromotive forces generated in the integrated circuits, which reinforces the efficiency of the attacks by fault injections. This paper presents a complete model of the electromagnetic field induced at the target surface according to Biot and Savart's law. This work defines the relevant design parameters of the new probes that are used for hardware characterization of the target components. These new probes reduce the voltage fault threshold required to disturb the execution of a program in the target. This paper also presents results related to the optimization of spatial resolution and inductive power at the target circuit surface. Understanding these phenomena then helps to implement countermeasures and best secure the strategies of the key IC components.

Integrated circuits (ICs) use cryptographic algorithms to secure their operations and communications. Almost all algorithms implemented in ICs are standardized [START_REF][END_REF], [START_REF]Advanced Encryption Standard (AES) FIPS[END_REF] and are free of mathematical security flaws. However, codes are still vulnerable to physical attacks targeting their implementation on ICs. The voluntary disruption of the operating environment of a target can corrupt the execution of a code, which can create errors (also called faults). An attacker can then bypass security mechanisms, obtaining personal data and the secret keys of encryption algorithms. This disruption is achieved by generating an EM pulse near the processor [START_REF] Dehbaoui | Electromagnetic Transient Faults Injection on a Hardware and a Software Implementations of AES[END_REF]. EM fault injection is generally performed with a voltage pulse generator, an injection probe placed on a motorized arm (allowing XYZ positioning), and a control computer as shown in Figure 1. The injection probe is usually made up of a few turns of a conductive wire around a ferrite rod. A voltage pulse delivered to the injection probe induces the EM perturbation. This field couples with the power-ground network of the target, causing a variation of its supply voltage and an alteration of its functioning. The design of the injection probe is therefore essential for a successful characterization, as detailed in [START_REF] Gaine | Electromagnetic Fault Injection as a New Forensic Approach for SoCs[END_REF]. To guide this design, a modelling of the probes and a method to compare the probes is proposed. The effect of the various parameters of the probe, including the effect of a ferrite material, is studied here. The dynamic study of the generator/probe combination makes it possible to define the specifications of new probes, which are more efficient than the state-of-the-art.

II. STATE-OF-THE-ART

Physical attacks are based on observing the operation of software code with and without its disruption. This first type of attack, also called fault injection (FIA), can be done by modifications in the operating environment such as temperature increases [START_REF] Skorobogatov | Local heating attacks on flash memory devices[END_REF], changes in supply voltages [START_REF] Timmers | Escalating Privileges in Linux Using Voltage Fault Injection[END_REF] and clocks [START_REF] Korak | On the effects of clock and power supply tampering on two microcontroller platforms[END_REF] generated by laser [START_REF] Vasselle | Laser-Induced Fault Injection on Smartphone Bypassing the Secure Boot[END_REF] or electromagnetic pulse disturbances.

The first experimental realization of an EM induced FIA was done by Schmidt and Hutter [START_REF] Schmidt | Optical and EM Fault-Attacks on CRTbased RSA: Concrete Results[END_REF] on an 8-bit microcontroller using sparks induced by a spark gap generator made from a gas lighter. However, this approach suffered from a lack of spatial and timing accuracy which was later improved using voltage pulse generators and coil-shaped EM injection probes. Dehbaoui et al. [START_REF] Dehbaoui | Electromagnetic Transient Faults Injection on a Hardware and a Software Implementations of AES[END_REF] realized the first fault injection with an electromagnetic pulse on both software and hardware implementation of the AES encryption algorithm. They were able to extract the AES encryption keys. Omarouayache et al. [START_REF] Omarouayache | Magnetic Microprobe Design for EM Fault Attack[END_REF] modeled and simulated magnetic probes for fault injection to deduce the effects of different parameters. They showed that the flux intensity depends on the distance between the probe and the circuit. They also suggested that a single wire loop can optimize the flux intensity and that the addition of a tapered ferrite tip improves the magnitude of the magnetic field delivered to the target.

Chusseau et al. [START_REF] Chusseau | Electromagnetic analysis, deciphering and reverse engineering of integrated circuits[END_REF] demonstrated that several turns allow better coupling between the injection probe and the target at low frequencies and that the addition of a ferrite material improves the intensity of the EM flux.

Beckers et al. [START_REF] Beckers | Design Considerations for EM Pulse Fault Injection[END_REF] showed that an increase in the number of turns decreases the amplitude of applied generator voltage, Toulemont et al. [START_REF] Toulemont | A Simple Protocol to Compare EMFI platforms[END_REF] presented a protocol for comparing Electromagnetic Fault Injection platforms with a commercial probe. They explained that the use of a Transil diode limits the bounces of the voltage pulse in the probe, thus increasing the timing accuracy.

III. TESTING PROTOCOL AND METHODOLOGY

The voltage pulse generators used can deliver pulses up to several hundreds of Volts with currents up to ten Amperes in a 50 Ω load. The rise and fall times are about 2 ns, while the duration of the pulse can be set between 10 ns and 100 ns.

An injection probe consists of a coil made of copper wire (coated with an insulator to avoid short-circuits between adjacent loops) wound around a ferrite rod. It is connected to the voltage pulse generator (as its load) and positioned in the close vicinity of the target. A picture of a state-of-theart probe is given in Figure 1.b. In order to experimentally compare the properties of the injection probes we studied, we set up a protocol that uses three types of targets: (1) other EM probes used as targets and two ICs: (2) an ATMega328P microcontroller and (3) a Zynq FPGA.

1) Probes used as targets: To measure the EM field induced by a given injection probe, we use two EM probes. The first one is a commercial RF-B probe from Langer with a diameter of 3 mm that makes it possible to record calibrated measurements of the overall intensity of the received EM field. The second one is a precise tiny home-made probe, 250 µm in diameter, considered as almost spot probe for local measurements.

2) Microcontroller ATMega328P: This 8-bit RISC microcontroller is present on Arduino Uno prototyping platforms. Its technology is CMOS 0.35 µm. It runs at 16 MHz. It was used to compare the ability of various injection probes to inject faults into a dedicated test code: it writes and reads data into and from the core's registers. We defined a fault threshold as the minimum voltage pulse magnitude that induces an EM perturbation capable of injecting faults into the target's registers. We use it as a metric to compare different designs of EM injection probes.

3) FPGA Zynq-7010: We embedded and targeted a ringoscillator-based sensor developed by Gravellier [START_REF] Gravellier | High-Speed Ring Oscillator based Sensors for Remote Side-Channel Attacks on FPGAs[END_REF] in the FPGA target. When exposed to an EM pulse, the supply voltage of the FPGA undergoes variations of its core voltage. Thus, the propagation delays of its logic gates evolve according to the intensity of the disturbance, which generates fluctuations in the output values of the sensor. This provides an image of the voltage variation inside the target. This sensor acts as an internal oscilloscope which measures the variations of voltages induced in the target.

IV. PARAMETERS TO CONSIDER WHEN DESIGNING AN EM INJECTION PROBE

A. Modeling of the magnetic field

Although the disturbance is mostly called electromagnetic, it is only inductive and not capacitive, so we can only consider the B field. The modeling of this field, for a point in space given by its (x,y,z) coordinates, can be calculated using Biot and Savart's law:

B z (x, y, z) = µ0I 4π N -1 n=0 2π 0 ((R+n * ζ) 2 -(R+n * ζ) * y sin θ-(R+n * ζ) * x cos θ)dθ [(x-(R+n * ζ) * cos θ) 2 +(y-(R+n * ζ) * sin θ) 2 +(z+n * δ) 2 ] 3 2
(1) ζ and δ represent the vertical and horizontal distance between two turns, R the radius of the coil, Θ the angle between the X axis and an elementary portion of the wire, as shown in Figure 2.a. I is the intensity of the disturbance and N the number of turns.

In Figure 2.b, where the field strength is shown as a function of x, it can be seen that an increase in the number of coils raises the strength of the disturbance. The solid lines represent the conical turns and the dotted lines the cylindrical ones, enabling the effect of conical versus cylindrical probes to be compared. A conical probe has a smaller spatial extent and a slightly higher generated field value than a cylindrical one. Therefore, the conical probe with 10 turns seems, on a theoretical basis, the most relevant for our parameters. These studies are done for a constant current I. However, in practice, ohmic law implies that an increase in wire length due to the number of turns or geometry will limit the current I. Even if it is preferable to have the smallest possible radius, shaping the tip of a probe into a conical shape improves the localization of the flux and the value of the generated field, as presented in Figure 2.c, with 5-turn probes. An angle at the tip is best for maximizing the generated field. However, even if the interdependent relations between the optimal values of radius R, number of turns N , δ, ζ and distance z to optimize the flux have not been clearly established, they can be determined iteratively by simulations as presented in IV-D. An angle of 120°is a first approximation given by the simulation.

From the formula, it can be seen that the space between two turns needs to be minimized to strengthen the field at the point of interest nearby, outside the probe.

B. Effect of a ferrite material 1) Presence of a ferrite material: In the literature, some probes are ferrite-based while others are not. We want to experimentally determine the effect of a ferrite material, and ascertain whether its presence is necessary. Currently, in the production of probes, a parameter limiting the reduction of the diameter of the probes is the presence of ferrite that is too brittle for small diameters. However, the reduction of the diameters of the probes can increase the intensity of the disturbance; we therefore want to verify that we should expect the presence of a ferrite material to enhance the magnetic field and generate faults. Our first experiment was designed to test whether it is useful to have a ferrite core in an injection probe. We measured the maximum voltage magnitude induced in the 250 µm target probe by 1 loop 3 mm diameter injection probes with or without a ferrite material for the same voltage pulse. Figure 3.a provides the induced voltage magnitude as a function of the off axis distance between both probes. Note that the curve for the ferrite-free probe is normalized (i.e. multiplied by 2.2) w.r.t. the probe with a ferrite core in order to better compare the shapes of their respective field pattern. This practical experiment showed that using a ferrite core improves the induction phenomenon by more than a factor of 2 with no significant effect on the field radiation pattern. It may therefore be necessary to choose a probe adapted to the distance from the target. A probe with a thin diameter, less than 250 µm for example, will have limited disturbance for a target at 500 µm. Figure 3.b depicts the effect of the 3 mm diameter probes on the FPGA sensor. The induced disturbance on the target core supply appears to be clearly diminished when a ferrite free probe is used. These results prove that the presence of a ferrite material is necessary to maximize the transient magnetic flux and inductive effect on the target.

2) Ferrite material: There are different types of ferrites; in order to maximize the generated fields, we studied 3 different types: Reference ferrites in common use (as in several publications [START_REF] Menu | Experimental analysis of the Electromagnetic instruction Skip Fault Model[END_REF]) Fair-rite 67 ferrites composed of nickel and zinc alloys, with a high quality factor up to 50MHz Fair-rite 78 ferrites composed of manganese and zinc alloys, for power applications up to 200kHz The FPGA-based test circuit is used to compare measurements between ferrite 67, 78 and reference probes for various diameters. The measurements shown in Figure 3.c present the maximum recorded value of Ring Oscillators during a spatial scan. The results for a 1500 µm ferrite diameter are shown, but they are similar for the other diameters. The inductive disturbance is higher with ferrite 78 type probes than with ferrite 67 and reference type probes. The Fair-rite 78 material exhibits the best performance compared with other ferrites.

The decrease of the magnetic field as the distance between the probe and its target increases is similar whatever the type of ferrite. The losses are about 15% for a distance of 200 µm and 30% for a distance of 500 µm with a probe using a ferrite of 1500 µm in diameter.

C. Dynamic study for the probe/generator combination

In our experiments, we used a voltage pulse generator from AvTech, the output impedance of which switches from 50 Ω to 1k Ω about 2 ns after the voltage pulse ends. Fig. 4.a provides the schematic of the SPICE model we used to simulate the voltage pulse generator and the injection probe (the parameters of the injection probe, a 200 nH inductance with a serial 0.1 Ω resistor in parallel with a 10 pF capacitor, were obtained from various measurements). A 150 Ω resistor is added between the probe and the pulse generator in order to easily measure the current across the probe.

The voltages at the probe, obtained with simulations and experimentally are shown in same tendencies, even if we do not observe as many bounces in practice. The simulation is consistent with the experiment during the pulse; we can therefore consider this model to properly describe the variation of the current according to different parameters. The variation in current will determine the variation in magnetic flux and therefore the electromotive force within the target.

1) Effect of inductance: Since an increase in the number of turns increases the inductance, it is necessary to know how this influences the current variation. The simulation, in Figure 4.c, shows that decreasing the inductance increases the voltage across the probe and shortens the disturbance. Thus, minimizing the number of turns could improve the intensity of the disturbance. However, it has previously been seen that an increase in the number of turns strengthens the intensity of the disturbance. These two factors balance each other, but in order to keep a rise time roughly lower than 2 ns, it is necessary to keep an inductance lower than 100 nH. The best compromise is to stay close to this value.

2) Effect of resistance: Changing the diameter or length of the lead wire affects the resistance. When we simulate the addition of a series resistance, the current variation decreases. However, between 0 and 10 Ω, the fall is limited to 5%. The resistance generated by a wire ranging between 40 µm to 250 µm in diameter varies from 1.38 Ω to 30 mΩ. This parameter is therefore not very relevant and the reduction of the wire diameter and thus the diameter and the length of the solenoid leads to successful optimization.

D. Conclusion

The above results allowed us to understand the mechanisms involved in inductive generation and to define rules for the design of the probes best suited for a given distance from a target:

• Use of a ferrite material, Fair-rite 78 for example • Maximization of the number of turns keeping an inductance value below 100 nH • Diameter of the probe chosen according to the distance from the target • Conical geometry with close-wound turns to improve disturbance locality and intensity • Wire as thin as possible, 40 µm to 100 µm in diameter TABLE I: Effect of overlaying on different sensors Now that we have identified the best probe parameters to optimize the energy transferred from the generator, we can use these results to make high-performance probes. We built a utility program tool, based on formula (1), that simulates the magnetic fields generated by the probes. It helps to achieve, by simulation, the best ferrite diameter and vertex, depending on the number of turns and the distance z to the target. This tool makes it possible to imagine and test new probe geometries.

V. NEW DESIGN FACTORS OF EM PROBES

With successive runs of the utility program, probe design alternatives have emerged. A conical geometry is more effective at performing fault injections than a simple cylindrical geometry. We evaluate hereafter the behavior of various alloys of ferrites and coil geometries.

A. Overlaying of coils

One of the limiting parameters of an injection bench is the maximum voltage of the generator. By making the probes more compact, i.e. by reducing the length of the solenoid, it is possible to reinforce the disturbance without increasing the drive voltage. To do this, a possible geometry consists in overlaying several coils, as shown in Figure 6.a (b) and (c). The simulation tools provide, in Figure 5.a, the B fields obtained with different types of probes. We can see that an overlay of the coils increases the intensity of the disturbance. The characteristics of 9-turn cylindrical probes, 5+4 turn (overlay of 4 turns on top of 5 turns) probes and 4+3+2 turn (double overlay of 2 turns on top of a layer of 3 on top of a layer of 4) probes are presented in Table 1. The fault threshold reductions are a little less than expected because such coils are difficult to realize properly. The disturbances were measured with various probes and it can be seen that the temporal (Fig This reduction is equivalent to increasing the pulse voltage by 25%, which is not easily available when we are already operating at the highest pulse voltages together with the lowest rise times available on the market.

B. Radial probes

Another way to improve the field intensity is to overlay all the turns, so as to create radial probes, as presented in Figure 6.a (d) and 8.a. Figure 6.b is a cross section view along the X axis, showing that the disturbance generated by a radial probe, in red, has a much larger lateral field extension, meaning poor locality compared to cylindrical probes but with the same intensity. A good compromise is to have probes with an overlay, as shown by the orange curve. The experimental results of a characterization with the 250 µm diameter probe are presented in Figure 6.c and are in good agreement with the simulation. The 2-level radial probe, in orange, generates higher disturbances than a cylindrical probe. Its lateral field extension is slightly worse. For the ATMega328P target, the fault threshold is close to those of the cylindrical probes with double overlay. The experimental use is more complex because the probe is rather large-sized; it is thus difficult to be in contact with the target.

C. Tape probes

In certain cases, such as small technological nodes, it is useful to improve the locality of the probes while preserving similar disturbance intensities. One solution is to replace the copper wire with a copper tape. Three probes with a diameter of 2 mm and with 1, 5 and 9 turns were made.

The experimental results of a characterization by a probe of diameter 250 µm are presented in figure 7.a. The profiles of the tape probes are symmetrical and their lateral spread at 90% of the maximum signal is much reduced compared to a cylindrical probe. The differences in the measured field strengths are less than 15%, which suggests a screening effect of the outer turns from the inner turns. This type of tape probe is also validated on a microcontroller ATMega328p, with a fault threshold of 75 V against 80 V for a cylindrical probe with the same characteristics. An interesting aspect with these probes is that their measured inductances are 20% lower than those of probes made with a copper wire of 200 µm.

D. Wrapped probes

If the magnetic field has to be even more concentrated and a loss of efficiency is acceptable, it is possible to wrap the probe in a ferrite sheet layer and if necessary overlay the wrapped probe with a thin copper sheet, as presented in Figure 8.b. The results of characterization with a 250 µm diameter probe are shown in Figure 7.b. Lateral field extension is reduced, falling sharply to a width of half the maximum value of 2500 µm for the cylindrical probe, 2300 µm for the ferrite-wrapped probe and 2100 µm for the ferrite-copper-wrapped probe.

E. Field projected through the integrated circuit

The magnetic field lines must loop back at the ends of the coil. The target positioned at the end of the probe is thus disturbed by a portion of the magnetic flux. In order to maximize the vertical extension of the flux while keeping lateral extension at its minimum, it is conceivable to have the a. Effect of tabe probes b. Effect of probes with envelopes c. Guidance of EM field through the chip Fig. 7: Others designs field lines not quickly looping back to the other side of the coil, but through the target, as presented in Figure 7.c. The field intensity at the target is then maximized. This was done for an ATMega328p target where the back side was removed and a ferrite layer sheet introduced. The fault threshold is then reduced from 62 to 57 V with the ferrite sheet. This brings an additional gain of 10% of the threshold voltage and can be combined with the new probe designs.

VI. CONCLUSION

The combined characterization work with a custom made probe, a microcontroller and a ring oscillator implemented in FPGA enabled the analysis, understanding and improvement of the radiating pattern of the inductive probes from the point of view of both their spatial and temporal response and the intensity of the generated disturbing magnetic fields.

New test protocols were presented to compare the effects of different probes. This helped improve iteratively the probe specifications as regards the field spatial distribution as well as its disturbing efficiency. The presence of soft high permeability ferrite was proven to limit the requirement of high voltages. A small diameter ferrite material will limit the magnetic field generated by the probe and for a given distance z, the radius R can be chosen to optimize the generated field. The ferrite can be tapered at a certain angle, 120°for example, to concentrate the magnetic flux. The probe coils are preferably composed of several compact overlays, with the constraint that their inductance should remain lower than 100 nH in order to keep a short impulse response or temporal locality. The coils must be close-wound and placed at the tip of the ferrite rod to maximize the projected field intensity. Field projection can also be enhanced with soft ferrite material placed below the target component. All these adjustments add up to about 30% more efficiency in fault thresholds.

New

  Probe Design for Hardware Characterization by ElectroMagnetic Fault Injection Clément Gaine * , Jean-Pierre Nikolovski * , Driss Aboulkassimi * , Jean-Max Dutertre † I. INTRODUCTION

Fig. 1 :

 1 Fig. 1: Electromagnetic fault injection bench (a) with a conical probe (b)

Fig. 2 :

 2 Fig.2: Modeling of probes but this is slightly compensated by an increase in the EM field generated. An increase of the ferrite diameter reduces the amplitude of the disturbance, as the inductance and EM field depend on the radius of the solenoid.Toulemont et al.[START_REF] Toulemont | A Simple Protocol to Compare EMFI platforms[END_REF] presented a protocol for comparing Electromagnetic Fault Injection platforms with a commercial probe. They explained that the use of a Transil diode limits the bounces of the voltage pulse in the probe, thus increasing the timing accuracy.

  Fig. 3: Ferrite

  Figure 4.b. The curves have the a. Electronic circuit diagram b. Voltage across the probe c. Effect of the inductance on current Fig. 4: Dynamic study of the probe

  5.b) and spatial (Fig 5.c) field extensions are not modified, while the intensity of the disturbances is increased. As regards the target microcontroller, the fault threshold is reduced by approximately 25% with the double overlay probe. a. Simulation b. Langer probe c. Probe 250 µm Fig. 5: Overlay of the turns a. Cylindrical, cylindrical with an overlay, b. Simulation of radial probes c. Effect of radial probes conical with a double overlay and radial probe Fig. 6: Radial probes

  This work has been done to improve the efficiency of fault injections. It also proved to be valid in the context of sidechannel acquisitions. Tests have shown that bandwidth and signal to noise ratio of traces needed to recover encryption keys are similar to those of commercial probes. a. Radial probe b. Probes with envelopes Fig. 8: Probes


Rajani D Dhingra
email: rdhingra@uidaho.edu

Jason W Barnes

Robert H Brown

Bonni J Burrati

Christophe Sotin

Phil D Nicholson

Kevin H Baines

Rog N Clark

Jason M Soderblom

Ralf Jauman

Sebast Rodriguez

Stéphane Le Mouélic

Elizabeth P Turtle

Jason E Perry

Valeria Cottini

Don E Jennings

Observational Evidence for Summer Rainfall at Titan's North Pole

Methane rain on Saturn's moon Titan makes it the only place, other than Earth, where rain interacts with the surface. When and where that rain wets the surface changes seasonally in ways that remain poorly understood. Here we report the discovery of a bright ephemeral feature covering an area of 120,000 km 2 near Titan's north pole in observations from Cassini's near-infrared instrument, Visual and Infrared Mapping Spectrometer on 7 June 2016. Based on the overall brightness, spectral characteristics, and geologic context, we attribute this new feature to specular reflections from a rain-wetted solid surface like those off of a sunlit wet sidewalk. The reported observation is the first documented rainfall event at Titan's north pole and heralds the arrival of the northern summer (through climatic evidence), which has been delayed relative to model predictions. This detection helps constrain Titan's seasonal change and shows that the "wet-sidewalk effect can be used to identify other rain events."

Plain Language Summary Cassini arrived in the Saturnian system in the southern summers of 2004. As expected, the Cassini team observed cloud cover, storms, and precipitation on the south pole. Like Earth, Titan has an axial tilt (27 • ) and its seasons vary over its year (30 Earth years). Ever since this shift in season began, the Cassini team eagerly waited for observations indicating cloud cover and precipitation that went missing from the northern latitudes. Our rainfall observation at the north pole is a major finding for two important reasons. First, this discovery observation heralds the much awaited arrival of the north polar summer rainstorms on Titan. This atmospheric phenomenon has been delayed compared to the theoretical predictions and was perplexing Titan researchers and climate modelers especially because the north pole hosts most of Titan's lakes and seas. Second, it is extremely difficult to detect rainfall events on Titan due to its thick atmospheric haze and very limited opportunities to view the surface (and its changes). We have used a novel phenomenon-the smoothening of a previously dry, rough surface by a thin layer of fluid after rainfall, similar to a wet sidewalk-as evidence for rainfall events on the surface of Titan.

Introduction

A major objective of the Cassini Solstice Mission was to search for evidence of seasonal changes on Titan [START_REF] Ádámkovics | Widespread morning drizzle on Titan[END_REF]Tokano et al., 2006)-both atmospheric (clouds) and surficial (rainfall)-that were expected to occur as Titan moved toward the northern summer solstice in 2017. Cassini arrived in the Saturn system during southern summer (2004) and observed clouds and rainfall at the south pole [START_REF] Porco | Imaging of Titan from the Cassini spacecraft[END_REF]Schaller, Brown, Roe & Bouchez 2006;[START_REF] Turtle | Cassini imaging of Titan's high-latitude lakes, clouds, and south-polar surface changes[END_REF], consistent with general circulation models (GCMs; [START_REF] Schneider | Polar methane accumulation and rainstorms on Titan from simulations of the methane cycle[END_REF][START_REF] Tokano | GCM simulation of balloon trajectories on Titan[END_REF]. However, as northern summer approached, the increase in cloud activity in the northern hemisphere that was predicted by such models was not observed. In particular, models predicted an increase in the cloud, storm, and rain activity by 2016. Instead, only small, isolated patches of clouds over the north pole began appearing in 2014 (T104 and later flybys). 1). (d) Zoomed-in view of the north polar region from the T120 flyby annotated to identify the features. The BEF is marked by magenta arrows in the figure. The black dot marks the north pole. (e) Analog for the T120 BEF on a cloudy day after rainfall. The specular reflection at the boundary of a puddle can be seen as a bright speck, while the road's wetted surface is reflecting broadly at the right geometries. (f) Analog for the T120 BEF as mudflat in Utah's Bonneville salt flats.

While both Cassini and Earth-based telescopes [START_REF] Roe | Titan's clouds from Gemini and Keck adaptive optics imaging[END_REF][START_REF] Schaller | Dissipation of Titan's south polar clouds[END_REF] have observed clouds on Titan, rain has only been inferred through observed surface changes that require high resolution views. Although four instruments on Cassini were able to observe Titan's surface: the RADAR [START_REF] Elachi | Radar: The Cassini Titan radar mapper[END_REF], Imaging Science Subsystem (ISS; [START_REF] Porco | Cassini imaging science: Instrument characteristics and anticipated scientific investigations at Saturn[END_REF], Visual and Infrared Mapping Spectrometer (VIMS; [START_REF] Brown | The Cassini Visual And Infrared Mapping Spectrometer (VIMS) investigation[END_REF], and Composite Infrared Spectrometer (CIRS; [START_REF] Jennings | Composite infrared spectrometer (CIRS) on Cassini: Publisher's note[END_REF], only the VIMS and ISS instruments operate at short-enough wavelengths to observe surficial veneers like rainfall.

The ISS instrument observed Titan's surface through the CB3 filter at 0.93 𝜇m and detected surface darkenings associated with rainfall events at southern high latitudes near the beginning of the mission (southern summer; [START_REF] Turtle | Cassini imaging of Titan's high-latitude lakes, clouds, and south-polar surface changes[END_REF]) and later at equatorial latitudes close to the spring equinox [START_REF] Turtle | Rapid and extensive surface changes near Titan's equator: Evidence of April showers[END_REF]. Subsequent to each of these events, VIMS observed surface brightening over months to years after the presumed rainfall [START_REF] Barnes | Precipitation-induced surface brightenings seen on Titan by Cassini VIMS and ISS[END_REF]. In neither case could VIMS detect the initial darkening of the surface (likely due to timing and flyby geometries). CIRS in the past has detected seasonal changes in surface temperature variations [START_REF] Cottini | Spatial and temporal variations in Titan's surface temperatures from Cassini CIRS observations[END_REF].

Observation

Herein, we report the discovery of an extensive ephemeral feature (Figure 1) near Titan's north pole that was observed by Cassini VIMS during the T120 (7 June 2016) flyby and which had disappeared by the next flyby, T121 (25 July 2016, with similar observation geometry); 3 Titan days (48 Earth days) later. The ephemeral feature is distinct due to its brightness, especially at longer wavelengths (5 𝜇m) and covers an area of ∼120,000 km 2 (spreading across 12 VIMS pixels; bigger than any of the Great Lakes on Earth). The spatial sampling of these pixels is on average ∼130 km in the north-south direction and ∼50 km in the east-west direction. In addition to the spectral data from VIMS, we use data from the RADAR, ISS, and CIRS instruments to constrain the origin and nature of this anomalously bright, ephemeral feature that we henceforth call the bright ephemeral feature (BEF). The ISS and VIMS data provide spectral information, RADAR data provide geologic context, while the CIRS data provide insight into the regional temperatures.

The previous flyby, T119 (6 May 2016), occurred 2 Titan days before the T120 flyby, and showed cloud cover over the north pole in VIMS data (see SOM for an image of T119). Prior to this, the region had most recently been observed by VIMS during the T106 flyby ∼2 years earlier (24 October 2014), and the BEF was not observed (Figure 1a; see SOM for observation geometries). The ephemeral nature of the feature suggests that the BEF was formed by some transient, short-lived process at the north polar region of Titan, which distinctly brightened the region during T120 flyby. Later, the region resumed its usual spectral characteristics by the next flyby, T121 (Figure 1c). We propose that the BEF represents a broad specular reflection from a wetted surface brought about by rainfall.

Method

To study how quickly the BEF changed, we compared the region corresponding to the BEF in the T120 flyby with the next flyby, T121, and the prior flyby in which the region was visible, T106. Table 1 shows the observation geometries of the VIMS data cubes used. To rule out the possibility that we did not observe the BEF in T106 and T121 due to unfavorable geometry, we list the distance of the T120 BEF from the specular point in each flyby in Table 1. The distance of BEF from the inferred specular point for T106 and T121 (847 Note. It helps us determine the existence of this feature over time, and we conclude that it is an ephemeral feature. The inferred specular points of the flybys are tabulated. We also show the distance of T106 and T121 specular points from the BEF; sp. pt. means specular point. The fact that the distance of inferred specular point. BEF = bright ephemeral feature.

and 470 km) is marginally different from T120's (632 km). Given the small change in the distance between the BEF and T106, T121 specular points, we would have observed the feature if BEF was present on T106 and T121 flybys. This indicates that we do not see the feature in T106 and T121 flyby due to its ephemerality rather than observation geometry.

We create a VIMS color composite of the observation and overlay it on the RADAR map of the north pole of Titan to infer the geographic location of the BEF in Figure 2. We then create spectra of different spectroscopic units and compare their brightnesses in Figure 3.

When we compare the spectra of different units from the T120 observation in Figure 3b, namely, BEF, specular, clouds, evaporite, and land, we use spectra from the same cube to minimize the atmospheric effects due to observation geometry (see SOM).

The areas where we see the BEF in VIMS are observed at high phase and emission angles by ISS (at 0.93 𝜇m), which makes it difficult for ISS to detect any darkening or brightening associated with the region. CIRS observations of the region, before and during/after the rainfall event, do not provide clear indications of a temperature drop due to any rainfall-derived cooling of the region.

Hypotheses

Several mechanisms could potentially produce the reported spectral signature in VIMS data: clouds, fog, evaporites, direct specular reflections (i.e., reflections off large smooth surfaces), and broad specular reflections. In the following text, we consider the merits of each of these possibilities and demonstrate how all but the broad specular reflections can be ruled out.

The T120 flyby contains extensive clouds in addition to the BEF that serve as the basis for our spectral comparison. Although VIMS observes from 0.3 to 5.1 𝜇m in 352 spectral channels, Titan's surface is only visible through the atmosphere in seven narrow spectral windows, at 0.92, 1.06, 1.26, 1.57, 2.0, 2.7, and 5 𝜇m [START_REF] Brown | The Cassini Visual And Infrared Mapping Spectrometer (VIMS) investigation[END_REF]. VIMS data are expressed in terms of surface reflectance as I/F (where I is the observed radiance and 𝜋F is the incident solar irradiance). The surface and clouds on Titan show distinct spectral 10.1029/2018GL080943

responses [START_REF] Rodriguez | Global circulation as the main source of cloud activity on Titan[END_REF][START_REF] Rodriguez | Cassini/VIMS hyperspectral observations of the HUYGENS landing site on Titan[END_REF]. We incorporate these spectral response characteristics into a color composite (RGB = 5, 2, and 2.7 𝜇m; [START_REF] Barnes | Global-scale surface spectral variations on Titan seen from Cassini/VIMS[END_REF][START_REF] Sotin | Observations of Titan's northern lakes at 5 𝜇: Implications for the organic cycle and geology[END_REF] to facilitate the identification of various spectral units in the observation. Though also bright at 5 𝜇m, clouds are brighter at 2.7 𝜇m [START_REF] Griffith | Characterization of clouds in Titan's tropical atmosphere[END_REF][START_REF] Mccord | Composition of Titan's surface from Cassini VIMS[END_REF][START_REF] Rodriguez | Titan's cloud seasonal activity from winter to spring with Cassini/VIMS[END_REF] owing to their high altitude. The wings of the 2-𝜇m band of clouds also indicate altitude. As a result, the color composite effectively distinguishes clouds (purple in Figure 1d) from BEF (orange in Figure 1d).

Low-lying clouds or fog [START_REF] Brown | Discovery of fog at the south pole of Titan[END_REF], however, cannot be entirely ruled out simply based on spectral comparison of the BEF with typical high-altitude clouds. Near-surface fog is difficult to distinguish from bright surface features in spectra without a reliable atmospheric radiative transfer correction. However, both the bright and red (5 𝜇m) spectrum of the BEF (in Titan's atmospheric windows) and the fact that the BEF does not extend over nearby large lakes (where one might expect the humidity to be higher) argues against the possibility of a low-lying fog. Even if the latter case is true, the occurrence of a fog layer necessitates a wet (humid) source underneath. Thus, the wetting of land surface by rain is strongly supported, especially considering the large areal spread of the BEF.

Evaporites, direct specular reflections, and broad specular reflections are all surface phenomena. While broad specular reflections from a liquid surface can occur if the surface is roughened by waves [START_REF] Barnes | Cassini/VIMS observes rough surfaces on Titan's Punga Mare in specular reflection[END_REF] or nitrogen bubbles [START_REF] Hofgartner | Transient features in a Titan sea[END_REF][START_REF] Malaska | Laboratory measurements of nitrogen dissolution in Titan lake fluids[END_REF], a broad specular return from a solid surface requires smoothing of the surface at length scales comparable to the wavelength of light, as would occur if the surface were wet (like a wet sidewalk after rainfall). RADAR and ISS data observations (Figure 2) show that the BEF occurs over a solid land surface, bordering known lakes in some places: the northwestern edge of the BEF coincides with Lagoda Lacus (equivalent radius of ∼54 km). However, waves on Lagoda Lacus would be discrete, smaller than the lake area, and cannot cause the bright pixels. The BEF is ∼3 orders of magnitude larger than the lake.

A commonly observed unit, particularly in the north, are 5-𝜇m bright deposits observed to abut many filled and empty lakes that are believed to be evaporitic material, comprising deposits left behind when lakes evaporate (Figure 3b; [START_REF] Barnes | Organic sedimentary deposits in Titan's dry lakebeds: Probable evaporite[END_REF][START_REF] Mackenzie | Evidence of Titan's climate history from evaporite distribution[END_REF]. Two lines of logic, however, strongly disfavor evaporite deposits for the BEF. The first is the spatial extent. Evaporites typically only border the edges of lake-the deposit observed along the southern end of Ladoga Lacus spans an area of 300 km 2 (as observed during the T76 flyby, 8 May 2011) compared to the BEF, spanning an area of ∼120,000 km 2 . Second, and most importantly, no evaporites have been observed to form and then disappear within a window of only a few Titan days, as was observed for the BEF (Figures 1a-1c).

Direct specular reflections, which we define as the reflection of light off a surface that is smooth at scales both comparable to the wavelength of light and to the projected image of the Sun on the surface [START_REF] Barnes | A transmission spectrum of Titan's north polar atmosphere from a specular reflection of the Sun[END_REF][START_REF] Soderblom | Modeling specular reflections from hydrocarbon lakes on Titan[END_REF][START_REF] Stephan | Specular reflection on Titan: Liquids in Kraken Mare[END_REF], depend on viewing geometry and result in an unusually high I/F. In the T120 flyby we observe the direct specular reflection from the Sun (I/F of ∼2 in the 5-𝜇m spectral window) from the surface of Xolotlan Lacus at 82.7 • N, 78.6 • W.

We observe the direct specular reflection of the Sun (I/F of ∼2 in the 5-𝜇m spectral window) in the T120 flyby, at 82.7 • N, 78.6 • W from the surface of the lake, Xolotlan Lacus (Figure 2c), ∼632 km away from the BEF. As a sidenote, the specular point seems close to the BEF or wet sidewalk in the Earth analog (Figure 1e). This is due to the smaller angular distance between the specular point and the BEF as compared to T120 observation.

Even though the BEF does not occur at the specular point, it does show spectral similarities to direct specular reflections on Titan. We compare the spectrum of the BEF with those of sea, clouds, land, evaporites, and the direct specular reflection (Figures 3a and3b), all taken from the same flyby (T120) to minimize atmospheric effects (see section 3 for observation geometry). The direct specular reflection is the brightest "feature" at 5 𝜇m in the observation. The next brightest feature at 5 𝜇m (by 50%) is the BEF. A rough surface cannot, on its own, reflect specularly. However, surface wetting coats the irregular surfaces of the rough region resulting in a smoother surface than what is underneath. The spectral brightness and observation geometry immediately indicate that the BEF is a broad specular reflection due to smoothing of a surface that was otherwise dry.

Modeling Surface Roughness

In order to test our hypothesis, we model the BEF's surface roughness to characterize specular reflections from a macroscopically rough surface (Figure 4). We use a numerical planetary specular model [START_REF] Barnes | Cassini/VIMS observes rough surfaces on Titan's Punga Mare in specular reflection[END_REF][START_REF] Soderblom | Modeling specular reflections from hydrocarbon lakes on Titan[END_REF] with Gaussian-distributed slopes and azimuthal symmetry, for the same observation geometry as the T120 observation (Figure 4b).

For small roughnesses with RMS slopes of 𝜎 ∼ 2 • (Figure 4c), only the direct specular reflection at the specular point appears. As we increase the roughness parameter, 𝜎, the specular reflection spreads over a larger number of pixels, each pixel receiving lesser solar flux, resulting in a fuzzier reflection distributed over a broader region. Over an area equivalent to the BEF, the model-determined 𝜎 values indicate that the required slopes to get signals comparable to our observation are ∼12-14 • (Figure 4d). This is twice the 𝜎 value of the inferred waves in Punga Mare (liquid surface), which were determined using the same model, to be ∼6 • . Figure 4e shows that, at higher slopes, (∼24 • ) the reflections become independent of the roughness parameter and show the entire solar flux (I∕F max , see section 3) distributed over Titan's hemisphere.

10.1029/2018GL080943

Results and Discussion

Based on our detailed analysis of the Cassini data coupled with roughness modeling and testing the feasibility of various possibilities, we propose that the BEF represents a broad specular reflection from a rough, wetted surface-presumably brought about by rainfall (T120 flyby, 7 June 2016), 2 Titan days after the observed cloud coverage (T119 flyby, 6 May 2016). A rough land surface could be smoothed by a recent surface wetting due to a summer-rainfall event. Earth analogs of wetted sidewalks (Figure 1e) and a mudflat [START_REF] Clark | Detection and mapping of hydrocarbon deposits on Titan[END_REF]) in Utah's Bonneville Salt Flats (Figure 1f) broadly fit the BEF profile. The RADAR data show the area to be rough, variegated, and nonuniform (at scales of ∼2 cm). A wet-sidewalk region is wet on a solid but rough substrate that at the right geometries produces broad specular reflections. These help us conclude that the BEF would have properties similar to a wet sidewalk that arises from a recently wetted, solid and rough surface on the north pole of Titan.

Conclusion

The reduced and delayed cloud and storm activity at Titan's north pole as opposed to the model-predicted activity suggests that our current understanding of Titan's changing seasons is incomplete. Our reported observations represent the first documented rainfall event on the north pole of Titan. We discover this rainfall based on a novel technique "wet-sidewalk effect" (broad specular reflections from a smoothened, original rough surface). Identifying the location and timing of the rainfall offers important data points for Titan GCMs, helping constrain why the northern summer cloud activity is delayed relative to predictions-especially because the north pole hosts most of Titan's lakes and seas [START_REF] Hayes | The lakes and seas of Titan[END_REF]. Apart from helping us understand Titan's weather and long term climate, a broad specular reflection observation like this helps us derive the roughness of the solid surfaces on Titan. Surface roughness of a region holds clues to its geologic evolution and nature of surface interactions and even has implications for landing site evaluations for future missions [START_REF] Turtle | Dragonfly: Exploring Titan's prebiotic organic chemistry and habitability[END_REF] to Titan.

Figure 1 .

 1 Figure 1. Visual and Infrared Mapping Spectrometer wet-sidewalk color composite (R: 5 𝜇m, G: 2.7 𝜇m, B: 2 𝜇m) of Titan's north polar region showing the region corresponding to the bright ephemeral feature (BEF) in the flybys (a) T106, 24 October 2014 (b) T120, 7 June 2016, and (c) T121, 25 July 2016. The yellow box in c shows the disappearance of the BEF 3 Titan days later (see Table 1). (d) Zoomed-in view of the north polar region from the T120 flyby annotated to identify the features. The BEF is marked by magenta arrows in the figure. The black dot marks the north pole. (e) Analog for the T120 BEF on a cloudy day after rainfall. The specular reflection at the boundary of a puddle can be seen as a bright speck, while the road's wetted surface is reflecting broadly at the right geometries. (f) Analog for the T120 BEF as mudflat in Utah's Bonneville salt flats.

Figure 2 .Figure 3 .

 23 Figure 2. The figure is in a different orientation than Figure 1. Kraken Mare is in the bottom right as opposed to the bottom left in the previous figures. (a) RADAR map of the north polar region of Titan in Polar Stereographic projection. The yellow box indicates the region corresponding to the bright ephemeral feature (BEF) illustrating that the region is mostly solid land. The non-data regions are white. (b) Visual and Infrared Mapping Spectrometer infrared color composite (R: 5 𝜇m, G: 2.7 𝜇m, B: 1.3 𝜇m) representing the yellow-boxed region as in the RADAR map of the north pole. (c) Visual and Infrared Mapping Spectrometer infrared color composite (b; R: 5 𝜇m, G: 2.7 𝜇m, B: 1.3 𝜇m) overlain on the north polar map of RADAR (a) showing the BEF and specular point. The red arrow indicates the specular reflection point (82.7 • N, 78.6 • W) near Xolotlan Lacus. The magenta arrows indicate the BEF we observe in T120.

Figure 4 .

 4 Figure 4. (a) Modeled reflectance (I/F) variation with surface roughness for the broad specular reflection (BEF) observed during the T120 flyby. The modeled (magenta) reflectance peaks at roughness (𝜎) values of ∼ 14 • indicating that the BEF's surface roughness could be of that order. (b) T120 Cassini image cube CM1866022476 where the BEF is observed. (c) Model-generated synthetic images for the T120 observation geometry with a surface roughness parameter of 2 • reveals only the specular reflection. One thing to note is the scale in the synthetic images: As we increase the roughness or specular deviation angle, 𝜎, the specular reflection spreads over a larger number of pixels, each pixel receiving lesser solar flux for higher 𝜎, and hence, the scale changes. (d) 𝜎 of 12 • covers the extent of BEF. (e) 𝜎 of 24 • distributes the entire solar flux onto the Titan hemisphere.

Table 1

 1 Details of T106, T120 and T121 Flybys, Which Cover the Location of BEF Over Three Time Stamps

	Spatial sampling

Acknowledgments

The authors acknowledge support from the NASA/ESA Cassini Project. R. D., J. W. B., C. S., and J. S. acknowledge support from NASA Cassini Data Analysis and Participating Scientists (CDAPS) grant NNX15AI77G. R. D. is grateful to Shannon MacKenzie, Deepak Dhingra, Johnathon Ahlers, Robert Chancia, Matthew Hedman, and Subrata Chakraborty for manuscript suggestions and would also like to thank the Cassini team for all the years of profound work. The VIMS data are available at the PDS imaging node (https://pds-imaging.jpl.nasa .gov/volumes/vims.html). The RADAR data were obtained from (http://pds-imaging.jpl.nasa.gov/ volumes/radar.html). Thanks to Jani Radebaugh and the other reviewer for their constructive comments and helpful suggestions on an earlier version of the manuscript.