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Journal of Medical Entomology Andrew Monaghan 1
DEVELOPMENT, LIFE HISTORY Research Applications Laboratory 2
National Center for Atmospheric Research 3
PO Box 3000 4
Monaghan et al.: Energy balance Boulder, CO 80307 5
model for water-holding containers Phone: (303) 497 8424 6
Fax: (303) 497 8386 7
E-mail: [email protected] 8
9
WHATCH'EM: An Energy Balance Model for Determining Water Height and 10
Temperature in Container Habitats for Aedes aegypti and Aedes albopictus 11
12
ANDREW J. MONAGHAN,1,2 DANIEL F. STEINHOFF,1 MICHAEL J. BARLAGE,1 13
THOMAS M. HOPSON,1 ISAAC TARAKIDZWA3, KARIELYS ORTIZ-ROSARIO,4 14
SAUL LOZANO-FUENTES,5 MARY H. HAYDEN,1 AND LARS EISEN5 15
16 1National Center for Atmospheric Research, P.O. Box 3000, Boulder, Colorado 80307 17
2Corresponding author, e-mail: [email protected] 18
3African Risk Capacity, 11 Naivasha Rd, SunningHill, 2157, Johannesburg, South Africa. 19
4Institute of Technology of Engineering, Jose D. Perez School of Engineering, University 20
of Turabo, P.O. Box 3030, Gurabo, Puerto Rico, 00778 21
5Department of Microbiology, Immunology and Pathology, Colorado State University, 22
3195 Rampart Road, Fort Collins, Colorado 80523 23
24
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Abstract 25
The mosquito arbovirus vectors Aedes aegypti (L.) and Aedes albopictus (Skuse) 26
exploit a wide range of containers as sites for oviposition and development of the 27
immature stages, yet approaches for modeling container water dynamics have been 28
limited. We introduce WHATCH'EM, a state-of-the-science, physically-based energy 29
balance model of water height and temperature in containers that may serve as 30
development sites for mosquitoes or other container-inhabiting arthropods. We also 31
employ WHATCH'EM to model container water dynamics in three cities along an 32
elevation and climate gradient in México ranging from sea level, where Ae. aegypti is 33
highly abundant, to ~2,100 m, where Ae. aegypti is rarely found. WHATCH’EM is 34
driven with field-derived meteorological data from May-September 2011 and evaluated 35
for three commonly-encountered container types with volumes of 3.8, 18.9 and 208.2 36
liters. WHATCH’EM simulates the highly non-linear manner in which air temperature, 37
humidity, rainfall and clouds interact with container characteristics (shape, size, and 38
color) to determine water temperature and height, leading to results that are not always 39
intuitive and likely not simulated by standard empirical models. In general, simulated 40
water temperatures are higher for containers that are larger, darker, and that receive more 41
sunlight. While air temperature drives differences in the magnitude and daily range of 42
container temperatures among the three cities, sunlight exposure (which is modulated by 43
clouds and shading from nearby objects) also plays a first order role. WHATCH'EM 44
simulations will be helpful in understanding the limiting climatic and container-related 45
factors for proliferation of Ae. aegypti and Ae. albopictus.46
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Keywords: Aedes aegypti, Aedes albopictus, container, energy balance model, water 47
temperature 48
49
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The mosquitoes Aedes aegypti (L.) and Aedes albopictus (Skuse), the primary 50
vectors of dengue, yellow fever and chikungunya viruses, exploit a wide range of 51
containers as sites for oviposition and development of the immature stages (Gratz 1999, 52
2004; Gubler 2004; Focks and Alexander 2006). These containers can range in size from 53
small trash items (e.g., bottles and cans) to medium-sized buckets and tires to large water 54
storage containers such as barrels or drums, tanks and cisterns (Morrison et al. 2004, 55
Tun-Lin et al. 2009, Bartlett-Healy et al. 2012). Proliferation of the mosquitoes is aided 56
by the presence of containers that hold water of suitable temperature and nutrient content 57
for eggs to hatch and immatures to develop. Using Ae. aegypti as an example, successful 58
larval development can be impeded by water temperatures that are too low for 59
development to occur (8-12°C) or high enough to cause physical harm, through heat 60
stress, to the larvae (36-44°C) (Bar-Zeev 1958, Smith et al. 1988, Tun-Lin et al. 2000, 61
Kamimura et al. 2002, Chang et al. 2007, Richardson et al. 2011, Muturi et al. 2012). In 62
the field, Hemme et al. (2009) found that Ae. aegypti immatures were absent from water 63
storage drums, which are key productive containers in Trinidad, in which water 64
temperatures exceeded 32°C. The temperature optimum for Ae. aegypti larval and pupal 65
development, with short development times and high survival rates, is in the range of 24-66
34°C (Bar-Zeev 1958; Rueda et al. 1990; Tun-Lin et al. 2000; Kamimura et al. 2002; 67
Mohammed and Chadee 2011; Padmanabha et al. 2011a, 2012; Richardson et al. 2011; 68
Farjana et al. 2012). There also is a growing recognition that the magnitude of the daily 69
temperature range (i.e., fluctuations over the course of a 24-hour period) impact life 70
history traits of Ae. aegypti, including larval development time (Lambrechts et al. 2011, 71
Mohammed and Chadee 2011, Carrington et al. 2013). Other factors that can have 72
negative effects on larval development time or survival include poor nutrient content of 73
the water and intraspecific or interspecific resource competition (Braks et al. 2004, 74
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Juliano et al. 2004, Padmanabha et al. 2011b, Walsh et al. 2011). For rain-filled 75
containers, there are also distinct risks of a container drying out before the immature 76
stages can complete their development or of the container over-flowing and the 77
immatures being flushed out (Koenraadt and Harrington 2008, Bartlett-Healy et al. 2011). 78
Weather-driven simulation models for Ae. aegypti populations -- such as CIMSiM 79
(Container Inhabiting Mosquito Simulation Model) and Skeeter Buster -- are strongly 80
influenced by water temperature, which impacts several important components of the 81
models including the development times and survival rates of eggs, larvae and pupae 82
(Focks et al. 1993a, b; Cheng et al. 1998; Magori et al. 2009; Ellis et al. 2011). CIMSiM 83
simulates the dynamics of immature Ae. aegypti and water dynamics within user-84
specified container categories, accounting for shape (circular or rectangular), dimension, 85
presence or absence of lid, fill method (manual or rain), fill frequency (daily, weekly, or 86
monthly), drawdown frequency (daily, weekly, or monthly), if it was located under the 87
edge of a roof or similar device to capture rain water, and if it was in shade or sun (Focks 88
et al. 1993a, Ellis et al. 2011). The original version of CIMSiM used default values for 89
key characteristics of a given container category (Focks et al. 1993a), whereas a more 90
recent version allows the user to input data for the container categories to represent the 91
average characteristics and density of that container category in the focal location (Ellis 92
et al. 2011). The Skeeter Buster model is based on the general characteristics of CIMSiM 93
but operates at the level of individual containers and also incorporates stochastic events, 94
e.g., survival of individuals of Ae. aegypti within a cohort (Magori et al. 2009). 95
Perhaps the greatest limitation of these complex simulation models is the 96
continued use of simplistic empirical relationships to predict water temperature in and 97
water loss from containers based on ambient air temperature (daily maximum and 98
minimum), sunlight exposure, precipitation, relative humidity, and saturation deficit 99
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(Focks et al. 1993a, Cheng et al. 1998). Recent work has shown that physics-based 100
approaches toward modeling container water properties are promising for resolving the 101
complexities of container water dynamics (Tarakidzwa 1997, Kearney et al. 2009). In the 102
present study, we introduce a state-of-the-science, physically-based novel model, as 103
opposed to an empirical approach, to explore water dynamics in container habitats of 104
relevance for Ae. aegypti and Ae. albopictus. The model calculates the height and 105
temperature of water in a specified container at hourly (or sub-hourly) intervals by 106
solving the system of equations that governs the energy balance (i.e., heat and moisture 107
budget) of the container as a function of meteorological and user-prescribed inputs. This 108
approach allows a user to examine the highly non-linear manner in which air temperature, 109
humidity, rainfall and clouds or shading interact with a specified container to determine 110
the height and temperature of the water it contains. The model, henceforth called 111
"WHATCH'EM" -- the Water Height And Temperature in Container Habitats Energy 112
Model -- is designed to be driven by readily-available meteorological observations and 113
user-specifiable container characteristics, so that it can be easily applied by a variety of 114
users, and potentially integrated into other weather-driven modeling frameworks such as 115
CIMSiM and Skeeter Buster. 116
We recently conducted a field study to determine the abundance of Ae. aegypti 117
immatures in containers in twelve communities located along an elevation and climate 118
gradient in central México (Lozano-Fuentes et al. 2012). Three representative 119
communities along this gradient are Veracruz City at sea level with highly favorable 120
climatic conditions for the mosquito, Rio Blanco along the eastern slopes of the Sierra 121
Madre Oriental (~1,250 m) where the mosquito is moderately abundant, and Puebla City 122
in the central highlands (~2,100 m) where a few specimens of Ae. aegypti were 123
encountered but the climate appears to prevent the mosquito from proliferating. 124
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Mosquito abundance was strongly correlated with weather parameters along this 125
elevation and climate gradient, including positive correlations with average minimum 126
daily ambient air temperature, average daily minimum relative humidity, and total 127
rainfall, and negative correlations with daily ambient air temperature range, during the 128
30-d period preceding the mosquito survey in a given community (Lozano-Fuentes et al. 129
2012). These findings led us to speculate that low or greatly fluctuating water 130
temperatures in containers may be limiting factors for population build-up of Ae. aegypti 131
at the higher elevations. Therefore, we apply WHATCH'EM to explore water dynamics 132
in three commonly encountered container types – small buckets (3.8 liters), medium-133
sized buckets (18.9 liters) and large drums (208.2 liters) – at the three cities noted above. 134
WHATCH'EM is used to examine the impacts of shading, clouds, and container color on 135
the water height and temperature in the three container types and three locations. The 136
model is driven by meteorological observations taken in each city during our field season 137
from May-September 2011, the time of year during which environmental conditions are 138
best suited (i.e., with combined high temperature and substantial rainfall) for the 139
proliferation of Ae aegypti in the study area. 140
141
Materials and Methods 142
WHATCH'EM and Its Energy Balance Equations. WHATCH'EM calculates 143
the water height (analogous with water volume) and water temperature of a specified 144
container, based on the energy balance of the water and the container. The full model 145
documentation and source code can be obtained from Steinhoff et al. (2013). 146
The energy balance method is used to calculate heat and moisture exchanges 147
between the surface and atmosphere in numerical weather prediction models in order to 148
estimate the surface temperature and evaporation. A similar method is used here, 149
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adjusted for container geometries and thermodynamic characteristics. WHATCH'EM 150
requires as input a minimal amount of commonly-available meteorological data 151
(temperature, relative humidity, and rainfall) to produce water temperature and level 152
estimates. WHATCH'EM takes into account variable factors such as cloudiness, shading, 153
container size and thermal characteristics, and any manual container filling that may 154
occur. The energy balance is calculated for both the water and the container. The energy 155
balance for water is based on the following equation: 156
157
WS CSW LW LW H L CQ Q Q Q Q Q Q Q →↓ ↓ ↑ ↑ ↑ ↓= + − − − − − (1), 158
159
where WSQ is heat storage in water (representing the change of temperature of the water), 160
QSW↓ is downward shortwave radiation, QLW↓ is downward longwave radiation, QLW↑ is 161
upwards longwave radiation, QH↑ is sensible heat transfer, QL↑ is latent heat transfer 162
(evaporation), QC↓ is conduction between the container bottom and water, and QC→ is 163
conduction between the container side walls and water. The energy balance for the 164
container is 165
166
CS SW LW LW H CG CQ Q Q Q Q Q Q Q→ → ← ← →↓ ↓= + − − − + + (2), 167
168
where CSQ is heat storage in the container, QSW→ is sideways inbound shortwave 169
radiation, QLW→ is sideways inbound longwave radiation, QLW← is sideways outbound 170
longwave radiation, QH← is sideways sensible heat transfer, QG↓ is conduction between 171
the ground and the container bottom, and QC↓ and QC→ are the same as in (1). Figure 1 is 172
a schematic showing the terms in equations (1) and (2) relative to the water and 173
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container. All terms are in units of power (Watts), and the sign convention is that all 174
radiation terms are positive into the container or its water, sensible, latent and ground 175
fluxes are positive out of the container or its water; and conduction terms are positive into 176
the container. 177
QSW↓ is the downward solar radiation absorbed by the water through the top 178
opening of the container. The shortwave radiation absorbed into the water is that 179
component not reflected by water or blocked by shade or clouds. QSW↓ is calculated as 180
181
( )( )1 1t t wSWQ S A a β↓ = − − (3), 182
183
where St is the total downward shortwave radiative flux (based on solar zenith angle at 184
the user-specified coordinates for the site of interest, and the transmission of solar 185
radiation through the atmosphere which is a function of cloud cover), At is container top 186
opening area, aw is the reflectivity (albedo) coefficient of water (a function of the solar 187
zenith angle per Cogley 1979), and β is the shade fraction. 188
QSW→ is the solar radiation absorbed by the container side walls. It is composed 189
of two components -- solar radiation directly striking the container side walls and diffuse 190
solar radiation -- not reflected by the container. QSW→ is calculated as 191
192
( )( )1SW c b dQ a Q Q→ = − + (4), 193
194
where ac is the reflectivity coefficient of the container, Qb is the direct component 195
(accounting for the zenith angle of the sun), and the diffuse component Qd is a 196
combination of solar radiation reflected from the ground onto the container side walls and 197
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atmospheric scattering. Similar to (3), the Qb and Qd terms take into account the surface 198
area of the container and shading effects. 199
QLW↓ is longwave radiation absorbed by water through the top opening of the 200
container, emitted by the atmosphere, clouds, and any shading surface. The emitted 201
longwave radiation is dependent on the fourth power of temperature (through the Stefan-202
Boltzmann law) and properties of the emitting body. QLW↓ is calculated as 203
204
4(1 )t a a s sLWQ A T Tβ ε σ βε σ↓ = − + (5), 205
206
where εa is emissivity of the atmosphere -- itself a time-variable function of air 207
temperature, vapor pressure and cloud fraction per Prata (1996) and Crawford and 208
Duchon (1999) -- σ is the Stefan-Boltzmann constant, εs is emissivity of the shading 209
surface, and Ts is the temperature of the shading surface (assumed equal to the air 210
temperature). 211
QLW↑ is the longwave radiation emitted by water in the container into the 212
atmosphere above. It depends on the temperature and emitting properties of water. QLW↑ 213
is calculated as 214
215
4t w wLWQ A Tε σ↑ = (6), 216
217
where εw is emissivity of water and Tw is water temperature (from the previous time step). 218
QLW→ is longwave radiation absorbed by the container side walls, assumed to be 219
half each of the longwave radiation emitted by the atmosphere and ground. It is 220
calculated as 221
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222
( )4 40.5 0.5LW s g g a aQ A T Tε σ ε σ→ = + (7), 223
224
where As is surface area of the container side walls, εg is emissivity of the ground surface, 225
and Tg is the ground (soil) temperature. 226
QLW← is longwave radiation emitted by the container side walls to the surrounding 227
air and ground. It is calculated as 228
229
4LW s c cQ A Tε σ← = (8), 230
231
where εc is emissivity of the container and Tc is the temperature of the container (assumed 232
equal to the water temperature). 233
QH↑ is the sensible heat transfer (primarily from convection) between the water in 234
the container and the air above. We assume that in the sheltered areas where most 235
containers are found, wind speeds are low, and free convection dominates; this 236
assumption breaks down as the container becomes more exposed to wind. QH↑ is 237
calculated from Monteith and Unsworth (2008) (p. 161): 238
239
( )t a w aH
H
AC T TQ
r↑
−= (9), 240
241
where Ca is the heat capacity of air and rH is heat transfer resistance, itself a time-variable 242
function of the Nusselt number (Steinhoff et al. 2013). QH← is the sensible heat transfer 243
between the container and surrounding air. It is calculated similar to (9), except that it is 244
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computed based on the surface area and temperature of the container sides, and rH 245
employs a different Nusselt number representing the geometry of the container sides: 246
247
( )s a c aH
H
A C T TQ
r←
−= (10). 248
249
QL↑ is the latent heat transfer, associated with phase changes of water. 250
Specifically for this application, it is the heat supplied to vaporization of water in the 251
container to the air above, and represents a heat sink for the water in the container. It is 252
calculated from 253
254
( )t a sL
W
AC e eQ
rγ↑
−= (11), 255
256
where es is saturation vapor pressure, e is vapor pressure, γ is the Psychrometer constant, 257
and rW is the water vapor transfer resistance, which is assumed equal to rH used to 258
calculate QH↑ in (9) (Arya 2001, p. 247). 259
QG↓ is heat conduction between the bottom of the container and the underlying 260
soil and depends primarily on calculation of the temperature gradient between the soil 261
and the container: 262
263
( )b c gG
A T TQ
zk
↓
−=
∆
∑ (12), 264
265
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where Ab is the container bottom area, ∆z is the differential layer depth, and k is thermal 266
conductivity. The ratio of the last two terms is summed for the half the thickness of the 267
ground layer (zg, kg) and half the thickness of the container (zc, kc), under the assumption 268
that Tc and Tg occur at the middle of each volume. The default value of zg is 50 mm 269
because it is the midpoint of the 0-100 mm upper soil layer for which temperature data 270
are commonly available. 271
Qc↓ is the heat conduction between the water and the bottom of the container: 272
273
( )b w cC
A T TQ
zk
↓
−=
∆
∑(13), 274
275
where notations are as before, with the ratio of the last two terms summed for half of the 276
thickness of the container and half of the depth of the water. Similarly, Qc→ is the heat 277
conduction between the water and the sides of the container Qc→ is calculated as 278
279
( )s w cC
A T TQ
zk
→
−=
∆
∑(14), 280
281
with the ratio of the last two terms summed for half of the thickness of the container and 282
the half the diameter (i.e., the radius) of the water. 283
Once the heat storage terms QSW and QSC have been calculated using the water 284
container energy balance equations (1) and (2), the water height in the container and the 285
water and container temperatures are updated. First, the accumulated evaporation of 286
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water from the container is calculated from the latent heat transfer, QL↑, following 287
Monteith and Unsworth (2008, p. 255): 288
289
L
t w
Q tE
Aλρ↑∆= (15), 290
291
where ∆t is the time period of the accumulated evaporation, λ is the latent heat of 292
vaporization, and ρw is the density of water. The water height change is then calculated 293
based on the difference of evaporation and precipitation over the time period ∆t: 294
295
( )1 ( / )w t bh P A A MF Eβ∆ = − + − (16), 296
297
where ∆hw is the water height change, P is precipitation accumulated over the time period 298
∆t, ϐ is the shade fraction (precipitation received in the container is dependent on the 299
shade fraction), the ratio At/Ab accounts for the amount of rainfall that can enter through 300
the container top relative to the size of the container body, and MF is any manual fill. 301
Currently, the minimum water height allowed in the program, for numerical stability 302
reasons, is 15 mm. Below this, water temperature and all energy balance terms are set to 303
a missing value, and a constant evaporation rate is set (default is 0.02 mm/hour). If, 304
through precipitation or manual filling, water height returns above 15 mm, then 305
calculations are restarted with water temperature set to the initial water temperature 306
specified at the beginning of the simulation. 307
With updated water height, the change to the temperature of the water in the 308
container is calculated as 309
310
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WSw
t w w
Q tTt A h C
∆∆=
∆ (17), 311
312
where ∆Tw is the water temperature change, QSW is the heat storage term, hw is the 313
updated water height (note that t wA h is the water volume), and Cw is the heat capacity of 314
water. Similarly, the container temperature is calculated as 315
316
CSc
c c
Q tTt V C
⋅∆∆=
∆ (18), 317
318
where ∆Tc is the container temperature change, QSC is the heat storage term, Vc is the 319
volume of the container material, and Cc is the heat capacity of the container material. 320
Input Data. There are three required meteorological variables, and two optional 321
variables for input to WHATCH'EM at hourly intervals. Required variables are: air 322
temperature (°C), relative humidity (%) and rainfall (mm hr-1). For this study, 323
temperature and relative humidity were obtained from low cost HOBO data loggers 324
(Onset Computer Corporation, Bourne, MA) installed in Veracruz City, Rio Blanco, and 325
Puebla City. For a map showing the locations of these cities in Veracruz and Puebla 326
States, México, see Lozano-Fuentes et al. (2012). Rainfall data were obtained from the 327
0.07° gridded Climate Prediction Center Morphing technique (CMORPH) dataset (Joyce 328
et al. 2004), which uses precipitation estimates derived exclusively from low orbiter 329
satellite microwave observations and features transported via spatial propagation of 330
information obtained from geostationary satellite infrared imagery. CMORPH provides 331
some of the most reliable estimates for tropical summer rainfall compared to other 332
satellite- and model-based rainfall products (Ebert et al. 2007). CMORPH data, which 333
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cover the globe from 60oS - 60oN, were bilinearly interpolated from the four surrounding 334
gridpoints to each HOBO site. 335
Optional variables include cloud fraction (low, middle, and high) and soil 336
temperature (°C). For this application, cloud fraction and soil temperature estimates are 337
obtained from the National Centers for Environmental Prediction North American 338
Regional Reanalysis (NARR, Mesinger et al. 2006). Gridded output with 32 km spacing 339
is bilinearly interpolated to each observation site and soild temperature is adjusted 340
(assuming a standard atmospheric lapse rate of 0.0065oC/m) for elevation differences 341
between the NARR topographic elevation and the observed elevation. Soil temperature 342
estimates are made at 50 mm depth. If cloud fraction data are not provided, then low, 343
middle, and high cloud fraction estimates are user-specified for both daytime and 344
nighttime conditions. If ground temperature data are not provided, then ground 345
temperature is estimated by the model using the near-surface air temperature 346
observations, based on the daily (24-hour) thermal wave, which is dampened and delayed 347
in time compared to the near-surface temperature daily cycle (Arya 2001). 348
Simulations. WHATCH'EM simulations were performed for Veracruz City 349
(19.2oN, 96.1oW), Rio Blanco (18.8oN, 97.2oW) and Puebla City (19.0oN, 98.2oW) for 350
three sets of experimental conditions. First, we used three container types: small buckets 351
(3.8 liters, 1 gallon), medium-sized buckets (18.9 liters, 5 gallons) and large drums (208.2 352
liters, 55 gallons) (Figure 2). For each container type the height, radius, thickness, and 353
thermal conductivity is user-specified to WHATCH'EM. Second, we evaluated three 354
colors for the containers: black, gray and white, corresponding to container albedos (ac) 355
of 0.1, 0.5 and 0.9, respectively. Container color is important primarily for the amount of 356
solar radiation absorbed by the container side walls. Third, we examined three levels of 357
shade: no shade, half shade, and full shade. Shade from natural objects (e.g., trees) or 358
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human-made structures (e.g., walls or roofs) affect both the long wave and short wave 359
energy balance and the precipitation received. 360
The simulations were run for two different scenarios with regards to containers 361
being filled with water: 1) with weekly manual container filling enabled (i.e., the 362
containers are topped off by human action every 168 hours), and 2) with manual filling 363
disabled (i.e., the containers only receive water through rainfall). For each of these 364
scenarios, the full set of combinations of the three experimental conditions described 365
above was performed, such that there are 3 x 3 x 3 = 27 total experiments per scenario. 366
The simulations were initialized for 0000 Coordinated Universal Time (UTC) on 1 May 367
2011, because May is near the end of the dry season in the study area but still precedes 368
the onset of the rainy season (in June or July) when Ae. aegypti populations are expected 369
to begin increasing. For the scenario in which there is no manual filling, the containers 370
are assumed to be dry at initialization on 1 May, after months of little or no rainfall. 371
Initial values for water temperature are also user-specified for the simulations with 372
manual filling since the containers are full from the onset. WHATCH'EM is integrated 373
once-per-minute from the initial time point through 0000 UTC on 15 September 2011 in 374
our simulations. This is an arbitrarily chosen time point that likely represents the latter 375
part of the active season for Ae. aegypti at the highest elevation examined, where the 376
climate in the winter is cold enough to prevent activity by this mosquito. Table 1 lists the 377
values of the constants and parameters that are used in WHATCH'EM. 378
379
Results 380
Climate Observations. The climates of Veracruz City, Rio Blanco and Puebla 381
City for May-September 2011 are compared in Figure 3. Monthly and total average 382
temperatures (Figure 3a) follow the elevation gradient between the cities, with Veracruz 383
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City, near sea level, being the warmest overall (29.0oC for the May-September average), 384
followed by Rio Blanco (~1,250 m above sea level; 21.3oC) and Puebla (~2100 m; 385
18.5oC). The average daily temperature range (Figure 3b) increases markedly along the 386
elevation gradient, being much lower in Veracruz City (3.9oC) versus the higher elevation 387
environments of Rio Blanco (9.0oC) and Puebla City (10.9oC). In contrast, relative 388
humidity does not exhibit marked variability between the cities during the May-389
September period (Figure 3c). In fact, the highest average relative humidity occurs in 390
Rio Blanco, where temperatures are cooler than in Veracruz City but the influence of 391
humid air from the Gulf of Mexico is still strong. However, the specific humidity (a 392
measure of absolute humidity that is independent of temperature) clearly shows that 393
Veracruz City is more humid than Rio Blanco, and that Puebla City is the least humid of 394
all the cities (Figure 3d). Likewise, the highest overall rainfall totals and cloud amounts 395
occur in Veracruz City (although the onset of rains is later there), followed by Rio Blanco 396
and Puebla City, which have similar rainfall totals and cloud amounts (Figures 3e-f). In 397
summary, during May-September Veracruz City is comparatively warm and humid with 398
a small daily temperature range and the greatest rainfall, whereas Puebla City is 399
comparatively cool and arid with a large daily temperature range and lower rainfall. Rio 400
Blanco’s climate is intermediate between Veracruz City and Puebla City. 401
Energy Balance Example for Rio Blanco. The results from WHATCH'EM for 402
the average May-September 2011 daily cycle of the components of the energy and 403
radiation balances are exemplified in Figure 4 for Rio Blanco, which has an intermediate 404
climate among the cities examined. The results are shown for a container with 405
intermediate values across our experiments: a gray, medium-sized (18.9 liter) bucket that 406
is located in half shade. Weekly manual filling was enabled in the presented scenario, so 407
the bucket is always full or nearly full of water. In Figure 4a, Bal stands for the WSQ term 408
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(equation (1)) and represents the heat gain or loss by the water that is manifested as a 409
change in temperature via equation (17). Short wave (solar, SW) radiation is the primary 410
driver of the energy balance during the day, while long wave (infrared, LW) radiation and 411
conduction (COND) between the container walls and water primarily drives heat loss at 412
night (Figure 4a). If the components of the LW and SW radiation are examined (Figure 413
4b), it is apparent that the horizontal components of both terms -- those that affect energy 414
exchange through the sides of the bucket -- are for this case on the same order of 415
importance as the vertical components that act through the top of the container. Figure 5 416
shows the average daily range (5a) and daily means (5b) for water, air and ground 417
temperature for the same gray, medium-sized bucket in Rio Blanco. The temperature of 418
the water in the container exceeds that of the air temperature on average due to the solar 419
radiation that is absorbed through the container sides during daytime, which is not 420
completely compensated by long wave and conductive heat losses at nighttime. The 421
magnitude of the SW and LW energy exchanges with the bucket are heavily influenced 422
by clouds and shading. During clear-sky periods (e.g., June in Figure 5b) the difference 423
between water and air temperatures is generally higher than during cloudy or rainy 424
periods (e.g., July) due to more solar absorption. 425
Experimental Results for Rio Blanco. Next we examine the results of the three 426
sets of experiments for Rio Blanco: comparisons of the average water temperatures and 427
water temperature fluctuations among (a) different types of containers with uniform color 428
and shading (Figure 6), (b) different colors of containers with uniform type and shading 429
(Figure 7) and (c) different levels of shading for containers with uniform type and color 430
(Figure 8). Manual filling was enabled for all experiments at Rio Blanco in the presented 431
scenarios in order to facilitate comparisons by minimizing the differences among the 432
containers that can arise due to water availability (in the manual filling experiments the 433
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containers are always nearly full). As shown in Figure 6, smaller containers, because 434
they have larger area-to-volume ratios -- i.e., more surface area available to exchange 435
heat with their surroundings compared to larger containers -- have the largest daily 436
temperature ranges. In this example, during drier conditions (May and June) the water in 437
the small bucket has an average daily temperature range of about 12oC, compared to 438
about 3oC for the water in the large drum. Counter-intuitively, the smaller containers 439
tend to have cooler average temperatures than larger containers, especially during clear 440
periods (e.g., June) because a greater fraction of the volume is exposed to nighttime heat 441
losses that are not fully compensated for by daytime heat gains. 442
As shown in Figure 7, the differences in reflectivity (albedo) among the various-443
colored containers cause substantial differences in daytime heating due to enhanced solar 444
absorption for darker colors; these differences are not fully compensated for during 445
nighttime since the albedo only impacts the solar (daytime) radiation balance. This 446
means that, compared to an otherwise identical white container, a black container will 1) 447
have a larger daily temperature range and 2) have a higher average water temperature. In 448
our example, the water in the black container is about 4oC warmer than the white 449
container on average. Differences in average daily temperatures between the no shade 450
and full shade cases are substantial: on the order of 10oC during clear-sky conditions 451
(May and June), and less (2oC) during cloudy conditions (July) (Figure 8). Additionally, 452
the no-shade containers have a much larger daily temperature range compared to shaded 453
containers (12oC versus 2oC) due to enhanced absorption of solar radiation. 454
Comparison of Results Among Cities. We also examined the differences 455
among cities for several experiments (Figures 9-11). Manual filling was disabled in the 456
presented scenarios to better understand the role of water availability in driving the 457
differences among containers, and therefore missing values represent times when water 458
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21
levels were <15 mm due to lack of rainfall. Figure 9 shows the May-September 2011 459
daily average, maximum and minimum water temperatures, and cumulative water 460
heights, for a gray, medium-sized (18.9 liter) bucket located in half shade for the three 461
cities. Figure 10 is a summary plot showing the May-September averages of water 462
temperature and the number of days with water heights >15 mm, by type of containers 463
and city. As expected, the daily water temperature decreases with elevation from 464
Veracruz City to Puebla City (Figure 9a). Conversely, the daily water temperature range 465
increases with elevation (Figure 9a), which is due to less cloudy conditions (Figure 3f) 466
and smaller volumes of water in containers due to lower rainfall (Figure 9b), in Rio 467
Blanco and Puebla City compared to Veracruz City. The May-September average water 468
temperatures in the containers (Figure 10a) are similar to the average air temperatures for 469
the same period (Figure 3a); this holds true for all three container types (all gray and in 470
half shade). However, it is noteworthy that the average temperatures become larger with 471
increasing container size (3.8 liter bucket versus 208.2 liter drum), with decreasing 472
albedo (black versus white), and with decreasing shade or cloudiness, as demonstrated in 473
Figures 6-8. 474
Moreover, the number of days with water heights >15 mm (Figure 10b) is 475
noteworthy because Puebla City, which receives the least rain (Figure 3e) and therefore 476
has the lowest cumulative water heights (Figure 9b), has the most days with water heights 477
> 15 mm. This is partly due to Puebla City receiving more rain earlier in the season 478
(May and June) in 2011. Therefore, despite having lower temperatures, water availability 479
does not appear to be a limiting factor for containers in Puebla City. Finally, the 480
histogram for number of days during May-September 2011 with daily water temperatures 481
falling within 2oC increments, based on a gray 18.9 liter bucket located in half shade, 482
illustrates the shift in typical water temperatures from low to high elevations (Figure 11). 483
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For example, water temperatures in the specified container commonly were projected to 484
exceed 24-26oC in Veracruz City but only very rarely in Puebla City. Conversely, water 485
temperatures commonly were projected to be <22oC in Puebla City, whereas this did not 486
occur in Veracruz City. 487
488
Discussion 489
We introduce WHATCH'EM, a state-of-the-science, physically-based energy 490
balance model of water height and temperature in containers. The model requires only 491
readily-available meteorological data from weather stations or atmospheric models and 492
user-specifiable container characteristics for input. It accounts not only for basic 493
container characteristics such as size and color, but also for shading, lidded containers 494
(not explored here), and mode of filling (rainfall only versus regular filing through human 495
action). WHATCH'EM complements, and ultimately should enhance, existing weather-496
driven simulation models for Ae. aegypti populations -- such as CIMSiM and Skeeter 497
Buster -- in that it greatly increases the realism of the estimates for the critically 498
important water temperature factor, which directly influences development times for the 499
immature stages of the mosquito and thus also the potential for population growth. 500
Although the main reason for developing WHATCH'EM was to support efforts to 501
determine the limiting factors for population growth of container-inhabiting mosquito 502
vector species, the model should prove broadly applicable to studies on other container-503
inhabiting organisms or physical processes related to the temperature of the water in a 504
container (e.g., the performance of chemicals added to the water, such as pesticides). 505
In our initial simulations, WHATCH'EM was applied to project water dynamics 506
in three commonly encountered container types (small buckets, medium-sized buckets 507
and large drums) at three representative cities located along an elevation and climate 508
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23
gradient that ranges from Veracruz City at sea level, where Ae. aegypti is highly 509
abundant, to the high elevation Puebla City at ~2,100 m, where Ae. aegypti is rarely 510
found (Lozano-Fuentes et al. 2012). Specifically, WHATCH'EM was used to examine 511
the impacts of container type, shading and clouds, and container color on the water 512
temperature and height, driven by meteorological observations taken in each city from 513
May-September 2011. We found that our energy balance modeling approach adds an 514
important level of complexity and non-linearity to water temperature variability, leading 515
to results that are not always intuitive and are likely not simulated by models that use 516
standard empirical approaches. To confirm this assertion, we ran the Cheng et al. (1998) 517
model which is currently used in CIMSiM to simulate water temperatures in a medium 518
bucket in no-shade conditions for our May-September 2011 study period (results not 519
shown). The Cheng et al. (1998) model, which does not account for cloud dynamics or 520
container color, simulates an increase in average daily water temperature range of 4oC 521
between Veracruz and Puebla versus an increase in WHATCH'EM of 10oC for a white 522
bucket, and 13oC for a black bucket. The greater sensitivity of the WHATCH'EM results 523
among cities is largely due to including cloud dynamics in WHATCH'EM. Accounting 524
for clouds in such models is also important from a climate change perspective: even if air 525
temperatures become warmer in a given location -- as they have nearly everywhere 526
globally and are projected to continue to do so (Intergovernmental Panel on Climate 527
Change 2007) -- changes in cloudiness (for which climate projections are highly 528
uncertain) have strong potential to amplify or dampen the corresponding changes in the 529
magnitude and daily range of water temperature in containers at that location. Changes 530
in the frequency and magnitude of rainfall also impact container water temperatures (by 531
modulating the volume) and the number of days in which adequate water is available for 532
development of mosquito immatures. In summary, climate change may have variable 533
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24
and unexpected impacts on the water characteristics in containers used by Ae. aegypti and 534
Ae. albopictus for oviposition and development of immatures. 535
The WHATCH'EM results for water characteristics in containers in the three 536
examined cities also provided insights into the mechanisms potentially underlying the 537
field observation that Ae. aegypti immatures are abundant at lower elevations (<1,300 m; 538
Veracruz City and Rio Blanco) but only rarely encountered at high elevations (>2,000 m; 539
Puebla City) (Lozano-Fuentes et al. 2012). Previous studies have shown that the 540
temperature optimum for Ae. aegypti larval and pupal development, with short 541
development times and high survival rates, is in the range of 24-34°C (Bar-Zeev 1958, 542
Rueda et al. 1990, Tun-Lin et al. 2000, Kamimura et al. 2002, Mohammed and Chadee 543
2011, Padmanabha et al. 2011a, Richardson et al. 2011, Farjana et al. 2012). We found 544
that model-projected water temperatures from May-September 2011 in a representative 545
container (gray, medium-sized bucket located in half shade) consistently exceeded 24°C 546
in Veracruz City and commonly exceeded 24oC in Rio Blanco, but very rarely did so in 547
Puebla City (Figure 11). Moreover, the model projected much greater daily temperature 548
ranges of the water in the containers in Puebla compared to Veracruz City (Figure 9a), a 549
factor that recently was demonstrated to be negatively associated with development time 550
of Ae. aegypti larvae (Mohammed and Chadee 2011, Carrington et al. 2013). 551
Consequently, we speculate that sub-optimal temperature conditions for Ae. aegypti 552
immatures in containers in Puebla City presently inhibits potential for population growth 553
of the mosquito in this high elevation city. 554
A somewhat surprising model result, given that Puebla City is located in the 555
comparatively cool and dry central highlands of México, was that Puebla City has the 556
most days with water heights > 15 mm for the simulated container under a rainfall-only 557
container fill scenario (Figure 9b) despite receiving the lowest total rainfall and having 558
Page 25
25
the lowest average relative and specific humidity (Figures 3c-e). This paradox is largely 559
due to greater early-season rainfall (Figure 9b) in Puebla City in 2011. Notably, the 560
indication from the model results that water availability in containers was not a limiting 561
factor for Ae. aegypti in Puebla City during the examined time period agrees with our 562
field observations, which produced similar numbers of water-filled containers per 563
examined premises in Puebla City versus a grouping of lower elevation communities 564
including Veracruz City and Rio Blanco (Lozano-Fuentes et al. 2012). 565
In conclusion, the WHATCH'EM model to estimate water height and temperature 566
in containers should prove a useful tool, separately and in combination with simulation 567
models for mosquito population dynamics, to further our understanding of the bionomics 568
of Ae. aegypti and Ae. albopictus. This paper focused on presenting the model itself and 569
our initial simulation results. To further demonstrate the realism of the WHATCH'EM 570
model estimates, a follow-up field validation study is underway in México. We also note 571
that WHATCH'EM simulations may prove useful for examining how human-572
environment-container interactions impact Ae. aegypti, for example by providing 573
information on which containers (by size, color and shading) have the most favorable 574
conditions for the mosquito and thus should be specifically targeted in source reduction 575
campaigns enacted by vector control programs or via community participation. Toward 576
this end, future work will more comprehensively assess the impacts of water storage 577
practices (i.e., manual filling) and container placement, shapes and types on water 578
characteristics. Finally, we also hope to be able to explore how WHATCH'EM, or a 579
related model building upon WHATCH'EM, could be applied to natural water bodies of 580
limited size, which may harbor a variety of mosquitoes of medical importance including 581
culicine arbovirus vectors and anopheline malaria vectors. 582
583
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Acknowledgments 584
We thank Carlos Welsh-Rodriguez, Carolina Ochoa-Martinez, Berenice Tapia-585
Santos, and Eric Hubron for field assistance. This study was funded by a grant from the 586
National Science Foundation to the University Corporation for Atmospheric Research 587
(GEO-1010204). The National Center for Atmospheric Research is funded by the 588
National Science Foundation. 589
590
591
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737
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Table 1. List of constants and parameters used in the WHATCH'EM model. 738
739
740
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34
Figure Legends 741
742
Figure 1. Schematic showing terms of energy balance model introduced in equations (1) 743
and (2). Terms are described in the text. (Online figure in color.) 744
745
Figure 2. Photos and dimensions (diameter x height) of containers used in the 746
WHATCH'EM simulations: (a) small bucket (3.8 liters, 1 gallon), (b) medium-sized 747
bucket (18.9 liters, 5 gallons) and (c) large drum (208.2 liters, 55 gallons). The three 748
colors (black, gray and white) used in the experiments are shown here arbitrarily by 749
container type. Additional container information can be found in Table 1. Photos are 750
reprinted from website of U.S. Plastic Corp., Lima, OH (http://www.usplastic.com). 751
752
Figure 3. Monthly data for selected climate variables for Veracruz City (red), Rio 753
Blanco (green) and Puebla City (blue) during May-September 2011. The “All” column is 754
the seasonal average or total over all months. (Online figure in color.) 755
756
Figure 4. Example from Rio Blanco of the average May-September 2011 daily cycle of 757
the components of the (a) energy balance and (b) radiation balance, based on water in a 758
gray 18.9 liter bucket in half shade. All components are expressed in Watts. Terms in the 759
legend are described in the text. (Online figure in color.) 760
761
Figure 5. Comparison of average daily range (a) and daily mean (b) of temperature, 762
from May to September 2011 in Rio Blanco, for the water in a container (green), the 763
container itself (orange), the air (blue) and the ground (red). This example is based on a 764
Page 35
35
gray 18.9 liter bucket in half shade. Terms in the legend are described in the text. (Online 765
figure in color.) 766
767
Figure 6. Comparison of daily average water temperature (solid lines) and maximum 768
and minimum water temperature (dotted lines), from May to September 2011 in Rio 769
Blanco, for gray containers in the form of 3.8 liter bucket (red), 18.9 liter bucket (green) 770
and 208.2 liter drum (blue) in half shade. (Online figure in color.) 771
772
Figure 7. Comparison of daily average water temperature (solid lines) and maximum 773
and minimum water temperature (dotted lines), from May to September 2011 in Rio 774
Blanco, for white (blue), gray (green) and black (red) 18.9 liter buckets in half shade. 775
(Online figure in color.) 776
777
Figure 8. Comparison of daily average water temperature (solid lines) and maximum 778
and minimum water temperature (dotted lines), from May to September 2011 in Rio 779
Blanco, for a gray 18.9 liter bucket in full shade (blue), half shade (green) and no shade 780
(red). (Online figure in color.) 781
782
Figure 9. Comparison of daily average water temperature -- solid lines -- and maximum 783
and minimum water temperature -- dotted lines (a) and water height (b), from May to 784
September 2011 and based on a gray 18.9 liter bucket in half shade, for Puebla City 785
(blue), Rio Blanco (green) and Veracruz City (red). (Online figure in color.) 786
787
Figure 10. Comparison of daily average water temperature (a) and days with water 788
height >15 mm (b), from May to September 2011 and based on a gray container (all three 789
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36
types are shown) in half shade, for Veracruz City (red), Rio Blanco (green) and Puebla 790
City (blue). (Online figure in color.) 791
792
Figure 11. Histogram of the total number of days from May to September 2011 with 793
water height >15 mm in a gray 18.9 liter bucket in half shade, by water temperature, for 794
Puebla City (green), Rio Blanco (red) and Veracruz City (blue). (Online figure in color.) 795
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38
a.
b.
c.
163 x 191 mm
597 x 921 mm
262 x 368 mm
Figure 2.
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39
05
101520253035
May Jun Jul Aug Sep All
Tem
pera
ture
(o C)
Month
a) Average Temperature (oC)
02468
101214
May Jun Jul Aug Sep AllTem
pera
ture
Ran
ge (o C
)
Month
b) Average Daily Temperature Range (oC)
0
20
40
60
80
100
May Jun Jul Aug Sep All
Rel
ativ
e H
umid
ity (%
)
Month
c) Average Relative Humidity (%)
0100200300400500600700800900
May Jun Jul Aug Sep All
Rai
nfal
l (m
m)
Month
e) Total Rainfall (mm)
VeracruzRio BlancoPuebla
0
0.2
0.4
0.6
0.8
1
May Jun Jul Aug Sep All
Clo
ud F
ract
ion
Month
f) Average Cloud Fraction
0
5
10
15
20
25
May Jun Jul Aug Sep AllSpec
ific
Hum
idity
(g k
g-1)
Month
d) Average Specific Humidity (g kg-1)
Figure 3.
