Dynamical controls on the diurnal cycle of temperature in complex topography Mimi Hughes Alex Hall Rob Fovell Baja California coast

A local perspective on the surface air temperature (SAT) diurnal cycle The simplest conception of the diurnal cycle of SAT is as a local energy balance between incoming surface solar radiation and net upward fluxes of sensible heat, latent heat, and longwave radiation. When the day begins, solar radiation exceeds these upward fluxes and the surface warms and stores energy. SAT reaches its maximum in the afternoon when increasing upward fluxes become larger than declining solar radiation. When the sun goes down upward energy fluxes cool the surface and SAT drops continuously, reaching its minimum at sunrise.

Spatial variation of the SAT diurnal cycle Spatial variability in the SAT diurnal cycle could arise from differences in surface type. In dry regions, small latent heat fluxes would reduce the damping effect of the net upward fluxes, and SATs would be more sensitive to solar forcing than in regions where the surface is wet. In fact, moderate diurnal amplitudes are observed in high soil moisture areas such as forests, while larger amplitudes are seen in more arid regions (Aires et al., 2004; Dai et al., 2004; Jin, 2004). Spatial variability in the SAT diurnal cycle also arises from variations in effective surface heat capacity, the most prominent example being the contrast between land and water. Over the ocean, for example, SAT diurnal cycle amplitude is virtually negligible compared to continents.

Land/Sea breeze Spatial variability in the SAT diurnal cycle leads to diurnally- varying thermal gradients. These in turn generate horizontal pressure gradients and diurnal cycles in atmospheric circulation. An example of this is the classic land/sea breeze circulation. Because of the difference in SAT diurnal cycle response between dry and wet land regions, one might also expect an analogous horizontal surface flow from relatively moist to dry regions during the afternoon, with corresponding flow reversal at night.

onshore flow during daytime

offshore flow at night

Diurnal Mountain winds Thermally-driven diurnal flows can also develop on a mountainous surface with a uniform SAT response to diurnal solar forcing simply because the surface is sloping (Rampanelli et al., 2004; Whiteman, 2000). This can be understood by considering a location on an idealized slope heated uniformly by the sun. The air adjacent to the slope warms significantly while the nearby free atmosphere at the same altitude does not warm as much. In a hydrostatic atmosphere this leads directly to a horizontal pressure gradient with an upslope component when projected onto the inclined surface. Thus, inclined surfaces typically experience upslope flow during daytime. Likewise, strong near-surface cooling induces downslope flow at night.

upslope flow during daytime

downslope flow at night

A simple picture of diurnal winds: bi-directional flow perpendicular to coastlines and elevation isolines in phase with diurnal cycle of temperature. daytime Sea breeze Upslope flow

A simple picture of diurnal winds: bi-directional flow perpendicular to coastlines and elevation isolines in phase with diurnal cycle of temperature. nighttime Downslope flow Land breeze

OBSERVED DIURNAL CYCLES OF SAT AND WIND

Locations of observations of wind and SAT, where enough data exists to create climatological diurnal cycles.

The shape of the observed diurnal cycle of surface air temperature is different depending on whether one is in the coastal zone or the desert interior.

12AM 3AM 6AM 9AM 12PM 3PM 6PM 9PM Observed diurnal winds At Point Mugu, winds are generally onshore during the day, and offshore at night, exhibiting slight clockwise rotation.

12AM 3AM 6AM 9AM 12PM 3PM 6PM 9PM Observed diurnal winds At Anza, winds are generally upslope during the day, and downslope at night, but they also exhibit clockwise rotation.

12AM 3AM 6AM 9AM 12PM 3PM 6PM 9PM Observed diurnal winds At Twenty Nine Palms, winds are generally upslope during the afternoon, and downslope at night, but they also exhibit clockwise rotation.

12AM 3AM 6AM 9AM 12PM 3PM 6PM 9PM Observed diurnal winds At Santa Barbara, winds are generally onshore during the day. However, the phase of the wind maximum occurs in the late afternoon.

EOF analysis The observed diurnal cycles of SAT can be conveniently summarized in terms of EOFs. Each EOF has an amplitude for every observation location as well as an associated time series.

EOF analysis EOF1 accounts for 96% of the SAT variance. It reaches its maximum in the mid to late afternoon and its minimum in the early morning. It can therefore be interpreted as diurnal cycle amplitude.

EOF analysis EOF2 accounts for just 2% of the variance. However its timing is about 90 degrees out of phase with that of EOF1. It represents the differences in the shape of the SAT diurnal cycle.

EOF analysis The observed diurnal cycles of SAT can be conveniently summarized in terms of EOFs. Each EOF has an amplitude for every observation location as well as an associated time series.

EOF analysis The observed diurnal cycles of wind can also be conveniently summarized in terms of EOFs. Each EOF has an amplitude and orientation for every observation location, as well as an associated time series.

EOF analysis EOF1 accounts for 62% of the wind variance. The vectors correspond to onshore and upslope flow, and the associated time series reaches its maximum in the mid to late afternoon and its minimum in the early morning. It can therefore be interpreted as the flow forced directly by the diurnal cycle of temperature.

EOF analysis EOF2 accounts for 29% of the variance. Its timing is about 90 degrees out of phase with that of EOF1. It represents rotation and variations in the timing of the maxima and minima of the diurnal winds.

EOF analysis The two EOFs are easily combined to regenerate the observed diurnal winds. 12AM 3AM 6AM 9AM 12PM 3PM 6PM 9PM

EOF analysis of SAT and winds

REGIONAL CLIMATE SIMULATION

Experimental Design model: MM5 boundary conditions: Eta model analysis resolution: domain 1, 54 km, domain 2, 18 km, domain 3, 6 km time period: 1995 to One can think of this as a reconstruction of atmospheric conditions over this time period consistent with three constraints: (1) our best guess of the large-scale conditions, (2) the physics of the MM5 model, and (3) the prescribed topography, consistent with model resolution.

Simulation Validation: SAT EOF analysis on the MM5 data, sub-sampled at the observation locations:  MM5 EOF analysis results in 2 EOFs which account for all variance (97%, 2%)  Associated time series agree very well  Spatial correlation of the loadings of the EOFs:  0.83 for EOF1  0.59 for EOF2

Simulation Validation: Winds Two EOFs which account for ~all variance (71% and 24%) Very similar associated time series Loadings of two EOFs also show good agreement MM5 Obs. MM5 Obs.

Results for full simulation: SAT EOF analysis of the full simulated SAT agrees well with both the sub-sampled simulation and the observations First two EOFs capture all variance, with similar proportions as sub-sampled model and observations Associated time series of full model field agrees with that from sub-sampled, and therefore with observations

EOF1 == SAT Diurnal cycle amplitude Largest at low elevations that are far from the coast To first order, what we’d expect from simple energy balance model (nearly zero over the ocean, large in arid regions, with maximum a few hours after noon) Small at high elevations, especially on coastal side of mountains

EOF2 == SAT Diurnal cycle phase and shape variations Where positive: SAT reaches an early maximum, and cools very little after ~9pm Where negative: SAT maximum is late in the day, and the air cools strongly through the night

EOF2 == SAT Diurnal cycle phase and shape variations Where positive: SAT reaches an early maximum, and cools very little after ~9pm Where negative: SAT maximum is late in the day, and the air cools strongly through the night EOF2<-1 EOF2>1

EOF2<-1 EOF2>1

Results for full simulation: Winds As for SAT, EOF analysis of the full simulated wind field agrees well with both the sub-sampled simulation and the observations First two EOFs capture all variance, with proportions similar to those for sub- sampled model and observations Associated time series of full model wind field agrees with that from sub-sampled, and likewise with observations

Wind EOF1: conforms to simple model of diurnal winds Generally see flow across coastline and isolines of elevation, resulting in convergence (divergence) at mountaintops during the day (at night) Flow associated with thermal gradients caused by differing land surfaces can overwhelm upslope/downslope tendency

Wind EOF2: rotation and phase variations Small in coastal areas, indicating a simple land/sea breeze in phase with SAT diurnal cycle Large in Mojave Desert, and west of Salton Sea. Winds there reach their maximum upslope (downslope) value at 10am (9pm). Also large south of Santa Barbara, where winds have a strong rotational component

Annual variation of SAT diurnal cycle The SAT diurnal cycle during February (and every calendar month) is very similar to that of August: Two EOFs explain ~all variance (although proportion changes slightly) Associated time series are very similar, except time spent going from min to max EOF1 shortens with the length of the day Spatial loadings of the two EOFs are reduced in winter months, due to reduced solar forcing

Annual variation of diurnal winds Like SAT, the February wind EOFs explain ~all variance, have very similar time series, and have similar, albeit smaller, spatial loadings.

Dynamical controls on SAT diurnal cycle The associated time series for the EOFs of SAT and wind are nearly identical, suggesting mechanistic links between the diurnal variability of the two variables. The dominant mode of wind variability is perpendicular to isentropes, affecting both the amplitude and the phase/shape of SAT diurnal cycle. This in turn could cause secondary wind anomalies, manifesting themselves as rotation and phase variations in the diurnal wind.

During the day, the sea breeze advects cool ocean air into coastal regions, suppressing maximum SAT. In the same way, the stable atmospheric stratification results in upslope flow bringing air with lower potential temperatures to high elevations.

At night, again because the atmosphere is stably stratified, downslope flow advects higher potential temperature air from high elevations downslope, and the divergence at mountaintops also brings warm air from above. This further reduces SAT diurnal cycle amplitude near the coast and in the mountains.

In the coastal zone, the advective daytime cooling caused by wind EOF1 shifts the time of day when surface cooling exceeds warming (that is, daily maximum SAT) to earlier in the day. Likewise, at night advective warming counteracts radiative cooling in coastal areas. In this way, wind EOF1 modifies SAT EOF2 as well as SAT EOF1.

In the desert interior, SAT EOF2 values are negative, indicating a late daily maximum and very strong cooling at night. This implies that the advective cooling (warming) during the day is not large enough to counteract the radiative forcing. This is because the interior atmosphere is less stably stratified, reducing the impact of upslope (downslope) flows.

The nighttime thermodynamic budget is to first order a balance between outgoing longwave radiation (a function of SAT) and advection. On the desert side of the mountains, advective warming is small because of weak stratification, and radiative cooling is large, resulting in strong cooling through the night. At mountain tops and on the coastal side, the more stably stratified atmosphere leads to larger advective warming, and the cooler temperatures result in less radiative cooling, with the net result being slow nighttime cooling, with SAT in some areas remaining constant after ~9pm.

The variations of SAT captured in EOF2 have a corresponding signature in the pressure gradient, which would drive a circulation similar to wind EOF2. Thus departures from the simple bi-directional model of diurnal winds are potentially caused by variations in the shape and phase of the SAT diurnal cycle.

Conclusions The dominant mode of diurnal variability for both SAT and wind primarily represents what we’d expect from simple models of these two variables. However, in regions with stable atmospheric stratification, the diurnal winds can advect potential temperature, moderating SAT diurnal cycle at high elevations and near the coast. Because atmospheric stratification is greater in the coastal zone than in the interior, the dominant mode of diurnal wind variability introduces spatial structure into the shape and phase of SAT diurnal cycle. In the coastal zone these winds shift daytime maximum earlier in the day, and prevent dramatic cooling at night. In contrast, the advective component in the interior is small, resulting in vigorous nighttime cooling. These variations in phase and shape of SAT in turn create secondary wind anomalies, resulting in rotation and phase variations in the diurnal winds.