A Trip Up Ka'ala 1: The Adiabatic Lapse Rate

Photo by Wendy Miles

One thing you may have noticed here in Hawai'i is that the windward sides of the islands are generally much wetter than the drier sides andf that the mountains towards the interiors of the islands are often cloaked in clouds.  For example, it may be bone dry in Honolulu when you get in your car to head up to Kailua or Kaneohe, but as you make your way through the back of Nu'uanu or Kalihi valleys you will likely encounter rain.  Then when you come out of the tunnel and drive down towards the beach, the rain starts to lessen and eventually you leave the clouds behind to enjoy your day at the Mokes or the Sandbar.  What explains this interesting weather pattern?  This first post in a series of three describing our recent trip up Mount Ka'ala, the highest point on Oahu (in the Waianae Range) aims to shed some light on issue.

The Problem...

Ah, the adiabatic lapse rate problem.

 If you've ever taken Geography 101 or the lab (or are currently taking them) at one of the UH system campuses, chances are you've seen this diagram.  The scenario is as follows: the wind blows from the northwest (1) into Hanalei Bay on the windward side.  The wind forces air up over Mt. Wai'ale'ale, which is one of the wettest places on the planet, and then it comes back down again in Waimea Bay, which is very dry, generally warmer than Hanalei Bay.  We see the same basic phenomenon on Oahu, Maui, and the Big Island as well.  To figure out why this happens, there are a couple of basic things we need to understand.

The Tradewinds

Lifted from NASA.

Our first step in understanding the problem is to understand the trade winds.  I am going to cop out a little bit here and say that we will discuss the trade winds in greater depth in a future post.  The important thing to understand here is that this is a pattern of prevailing winds in Hawai'i in which the wind blows from the northeast towards the southwest.  This pattern dominates our weather here approximately 80% of the time in the summer months, and from 50-60% of the time in the winter months.  The trade winds are why the weather is generally pleasant in Hawai'i, and they are caused by the general global atmospheric circulation.  The trades bring moist air from the ocean and force it up over the mountains.  The weather pattern described in the Mt. Wai'ale'ale problem is a function of the trade winds.

Humidity and temperature...

Our second step is to understand humidity.  We generally define humidity (very basically) as water vapor in the atmosphere (2).  The more water vapor you have in the atmosphere, the higher the humidity.  Though there are several ways to measure humidity, here we're going to focus on the relative humidity.  This is simply the amount of water vapor in the atmosphere relative to how much the atmosphere could potentially hold.  Think of the atmosphere as a glass.  A glass can be empty, or full, or partially full.  So we think of the size of the glass as the amount of water vapor that the atmosphere could potentially hold, and the amount of water vapor can be thought of as how much water there is in the glass.  Therefore the relative humidity is how "full" the glass is.  Under normal circumstances humidity ranges from 0% to 100%.  That's easy enough.

Now about that glass.....we can change its size.  The way we do this is by changing the temperature.  We have a simple relationship: the ability of air to hold water vapor depends on its temperature.  The higher the temperature, the more water vapor the air can hold, the lower the temperature, the less.  So if you increase the temperature the glass gets bigger, if you decrease it, the glass gets smaller.

There's another thing about this as well.  The glass doesn't get bigger or smaller at a constant rate.  As the temperature increases, the capacity of the air to hold water vapor increases exponentially.  That means the hotter it gets, the faster the glass grows, and the colder it gets, the slower the glass shrinks.  Check out the graph, which plots temperature (x axis) versus how much water vapor the air can hold (y axis).

So what happens if it keeps getting colder and colder?  The "glass" will get smaller and smaller.  Eventually it will get to the point where it can't hold the "water" anymore.  You can probably imagine what happens at that point: the water spills out of the glass.  A similar thing happens as the air gets colder.  Eventually you reach the 100% humidity level, and some of the water vapor has to "spill" out.  But in the case of air, the water vapor turns back into water.  This is how clouds form (clouds are water, not water vapor).  We'll have another post in the future about this topic.  But for now you can see what happens: the trade winds bring in moisture-laden air, forcing it up over the mountains.  As it rises it cools down, and as it cools it loses its capacity to hold water vapor, until eventually the air becomes saturated, meaning it is holding all the water vapor it can hold.  It is at this point that clouds begin to form.  If the air continues to rise water vapor continues to be converted back into water, and eventually there is so much water it will rain.

When the air reaches the top of Mt. Wai'ale'ale it starts coming back down the mountain, and as you might have guessed, it warms up as it moves down the mountain (3).  This means that it can hold more water vapor (the "glass" is getting bigger), and so instead of converting water vapor into water, the reverse process happens: water is evaporated into water vapor.  The clouds first start to evaporate; when all the clouds are gone any water on the ground starts to evaporate.  One thing we assume here is that whenever there are clouds, the humidity is 100%.  Clouds indicate that the air is saturated.

So What About the Temperature and Relative Humidity?

As the air moves up the mountain, the temperature decreases.  That part we know from experience.  The interesting thing is that it decreases at a constant rate.  We call this rate the adiabatic lapse rate.  When the relative humidity is less than 100%, this rate is about 5.5 degrees Fahrenheit per 1000 feet, or .55 degree per 100 feet.  If the air travels 1000 feet up the slope, the temperature will decrease 10 degrees; if it travels 1000 feet down slope, it will decrease 10 degrees.  This makes sense to us; this is why we sometimes find snow on the top of Mauna Kea.

The complex thing that throws everybody off (and it's not really that complex) is that the adiabatic lapse rate changes if the humidity is 100% (if the air is saturated).  We call the first lapse rate (5.5 degrees/1000ft) the dry adiabatic lapse rate (DAR); when RH% is 100% we use the moist adiabatic lapse rate (MAR).  The MAR is (in this example) 3 degrees Fahrenheit per 1000 meters.  Why is it lower?  The answer is simple, but you need to concentrate and think about it.  If the RH is 100% and the temperature continues to decrease, your "glass" is getting smaller and so water vapor must be converted into water.  But for every gram of water vapor that turns into water, a significant amount of heat is released into the atmosphere (the latent heat; this will be discussed in a future post).  This heating slows down the cooling trend you have with increasing elevation, and that's why the MAR is less than the DAR. Now we have all we need to know to tackle the problem.

If we start in Hanalei Bay at 80 degrees and follow our air parcel up, the

Does this guy look familiar?

temperature decreases by 5.5 degrees per 1000 feet.  Thus at 1000 feet the temperature is 74.5 degrees and at 2000 feet it is 69 degrees.  But we notice at 2000 feet that clouds are forming (the "glass" is full), which means that water vapor is being converted to water and heat energy is being released, which slows the cooling.  From this point we use the MAR of 3 degrees per 1000 feet.  Thus at 5000 feet the temperature is 60 degrees, and it is raining, raining, raining.  Then the air starts to go down the mountain, warming as it descends.  The "glass" is getting bigger, but it stays "full" because the air is evaporating the clouds.  Now remember that when you make clouds you release heat so the cooling decreases, but when you evaporate clouds you absorb heat energy, so the warming is slower.

So as we go down the mountain the temperature increases at a rate of 3 degrees per 1000 feet (the MAR) until we get to 3000 feet, which is the cloud base.  Remember that clouds mean 100% relative humidity, and so once you leave the clouds the relatively humidity is less than 100%.  You may have noticed that cloud base on the windward side is 2000 feet, whereas it's 3000 feet on the leeward side.  Why is this?  Because there is less moisture available on the leeward side.  There is less moisture available because it was raining on the top of Mt. Wai'ale'ale, and so some of that rain flowed down the mountain or infiltrated down into the soil, and so it is no longer in the atmosphere, and no longer available to be evaporated.

Therefore at 3000 feet we switch back to the DAR of 5.5 degrees per 1000 feet.  I'm not going to give away the answer which you should be able to calculate easily, but it should be clear here that the temperature is greater in Waimea bay than it is in Hanalei Bay.  It is also much drier, because the relative humidity is lower and the air is trying to evaporate moisture at this point, which leads to dry conditions.

What does this have to do with Mt. Ka'ala?

Map from Hawaii DLNR site on Ka'ala.

Funny you should ask.  A couple of weeks ago the crew responsible for this blog made a hike of Mt. Ka'ala, the highest point on Oahu.  We started off from the back of Waianae Valley and followed the well-marked trail all the way to the top, which took approximately 4 hours.  Along the way we took relative humidity measurements using a sling psychrometer, an instrument you're familiar with if you've ever taken or are currently taking 101 lab at UH, KCC, or HCC.  The wind conditions were atypical, meaning that the wind was light and variable.  Normally it is quite windy on the top of Ka'ala when the tradewinds are blowing.  Still, we noticed a temperature gradient consistent with what we would expect from the explanation above.  The temperature decreased at a steady rate with as we climbed.  We recorded the measurements in a notebook, and our intention was to provide a data table and graph, but on the way back down we got caught in a very heavy downpour and so our notebook got wet.  This is due to the fact that one of the geography crew forgot one of the most important tools for doing geographical fieldwork: a waterproof notebook.

Anyway, after eating our lunch and horsing around for a bit on thelee side of the mountain the air moves down the slope, warming along the way.  As it warms it can take on more water vapor.  First it evaporates the clouds, but since some of the air's moisture has been lost in the form of rain, the clouds are quickly evaporated.  This is why the cloud base on the lee side is higher than the cloud base on the windward side.  This is also why the lee side is usually quite dry; the air descending from the mountains is constantly evaporating available moisture.

Geography John demonstrating proper
sling psychrometer technique

top of Ka'ala, the wind started to change, bringing moist air off the ocean into the mountain, which is consistent with tradewind conditions.  As mentioned above, as the air rises over the mountain it loses its capacity to hold water vapor, which forces condensation and eventually it starts to rain.  On the way down we got drenched, but eventually we descended far enough so that we were out of the rain.  This should make sense given our understanding of how all this works; on the

That about does it for this post.  In our next post one of the geography crew will explain about the vegetation zones you typically encounter as your elevation increases in Hawai'i, providing some examples from the Ka'ala trip.  Stay tuned!

Key Terms

Gradient: a change of a particular variable over distance.  For example, the higher you go up a mountain the colder it is.  There is a strong temperature gradient.  Another example can be seen with rainfall; Hawai'i has very noticeable rainfall gradients.  If you start in Waikiki, there is very little rain, but once you make it to the back of Manoa valley it is very rainy.  There is a very sharp change over distance, hence a strong gradient.

Leeward:  The leeward side of the island is the one that the prevailing wind blows away from.  In Hawai'i the prevailing winds are the trades, which blow from the northeast and east, so the leeward side is the south and east sides of the islands.

Windward:  The windward side of the island is the one on which the prevailing wind blows.  In Hawai'i this is normally the northeast and east sides of the islands.  

Discussion Questions

Question 1:  If the temperature increases, what would happen to the relative humidity?  What about if the temperature decreases?

Notes

(1)  We would generally refer to this as a northwesterly wind.  We always name the wind for the direction from which it blows.  So a wind blowing from the south is a southerly wind, one from the east is an easterly wind, and so forth.

(2)  In geography we deal with water in three states: solid (ice), liquid (water), and gas (water vapor).  It is the last of these that concerns us here.  The air always has a certain amount of water vapor in it, and this water vapor is invisible.

(3)  Rising air cools, sinking air warms up.