Dewpoint depressions, relative humidity, and lifted condensation level

[Dan Ross]

I've been chasing for many years now. I've studied some mesoscale meteorology as it applies to thunderstorms/tornadoes, but I'm certainly no meteorologist. The three calculations in the thread title are things I've felt I understood pretty well, but the harder I think about them, the less clear things become:

So I know that generally speaking, the smaller the dewpoint depression, the higher the relative humidity, and the lower the lifted condensation level. Also I’m pretty sure that not all scenarios for a given DD represent the same RH - for example a 50/30 (T/D) and a 80/60 would not have the same %RH, right? Considering this, I would assume that both parcels, when lifted and cooled at the dry adiabatic lapse rate, would have identical LCLs because they’d both have to cool by the same amount to become saturated. So does this mean that calculating LCLs is as simple as knowing the DD, and that RH is less useful comparatively? Obviously I haven’t yet tried looking into the math behind it all. I guess I feel like it probably isn’t that simple, so could anyone here help shed some light on the interrelatedness of these 3 things?

 

[Dan Ross]

Yyyyyeah, didn't mean to post this thread twice...oops!

 

[Lou Ruh]

Well ... certainly not my area of expertise ... but, assuming http://www.aprweather.com/pages/calc.htm is a good source (probably is), it looks like what you are saying would produce a good approximation ... it shows:

LCL Height (Estimated FT)= H= 222(Tf-Tdf)

( Tf is temp in Fahrenheit and I believe Tdf is Dewpoint in Fahrenheit) and a similar estimate for LCL Height in meters. So, using Dewpoint depression works for an estimate. The actual computation is shown on that website and uses Surface Temp, Dewpoint and Pressure and does not yield the exactly same results for identical dewpoint depressions at the same surface pressure. And, I found a calculator at http://www.csgnetwork.com/lclcalc.html if you really want exact values.

 

[Dan Ross]

Thanks! That's a pretty handy estimator. If I enter 80/60 (T/D) into that calculator it gives a higher LCL than a 50/30, so the higher your T and D for a given dew point depression, the higher the LCL. For my purposes, that's mostly what I wanted to confirm. I've done a bit more reading as well, and it appears the truer way of dealing with it is in terms of "vapor pressure", rather than arbitrary temperature values, but that's probably beyond what's practical for my purposes as a chaser. I'll leave that to the meteorologists!

 

[Jeff Duda]

While there is definitely a strong correlation between dewpoint depression and LCL height, strictly speaking the two cannot be equated using a simple formula. The one presented above is merely the result of a statistical regression.

The reason there is not a perfect 1:1 correspondence between DD and LCL height is that the dry adiabatic lapse rate is not truly constant since it is defined as g/Cpd, where g is the gravitational "constant" and Cpd is the specific heat of dry air at constant pressure. Technically neither is truly constant, as Cpd has a slight dependency on temperature and g varies slightly with altitude.

Additionally, relative humidity is defined in terms of vapor pressure, and (saturation) vapor pressure is exponentially dependent on temperature, so for any fixed value of DD, RH can vary widely depending on the specific temperature and pressure.

For basic analysis, however, using DD or RH as a proxy for LCL height is just fine. The differences/errors are not going to be meaningful.

 

[Brett Roberts]

I've been chasing for many years now. I've studied some mesoscale meteorology as it applies to thunderstorms/tornadoes, but I'm certainly no meteorologist. The three calculations in the thread title are things I've felt I understood pretty well, but the harder I think about them, the less clear things become:

So I know that generally speaking, the smaller the dewpoint depression, the higher the relative humidity, and the lower the lifted condensation level. Also I’m pretty sure that not all scenarios for a given DD represent the same RH - for example a 50/30 (T/D) and a 80/60 would not have the same %RH, right? Considering this, I would assume that both parcels, when lifted and cooled at the dry adiabatic lapse rate, would have identical LCLs because they’d both have to cool by the same amount to become saturated. So does this mean that calculating LCLs is as simple as knowing the DD, and that RH is less useful comparatively? Obviously I haven’t yet tried looking into the math behind it all. I guess I feel like it probably isn’t that simple, so could anyone here help shed some light on the interrelatedness of these 3 things?

Short answer: you're correct that using dewpoint depression to estimate LCL height is more accurate than using RH for the same purpose.

Using dewpoint depression is "good enough" for any practical applications. In fact, even the formula is easy to remember:

H_lcl ~ (T-Td)/8,

where the dewpoint depression is in Celsius and the LCL height is in km. So a depression of 4°C corresponds to an LCL height of 0.5 km, and 8°C corresponds to 1 km.

An equivalent linear function of RH used to estimate LCL height would not be nearly as accurate. However, over the range of temperatures typically seen in convective forecasting and analysis (say, 10-35°C), a function optimized for that range would have errors on the order of 10% -- not bad enough to make it totally useless in a pinch.

 

[Dan Ross]

Thanks Jeff and Brett for the concise answers - exactly what I was looking for. I moved out to Fort Collins, CO this year after living in northern IL my whole life, so I'm seeing a lot more higher based storms than back east, along with some tornadoes in environments with lower dewpoints/higher LCLs. Anyway that's what got me thinking about all this. So basically the equations are non-linear, but for the range applicable to convective forecasting (as Brett mentioned), they are close enough that a simple linear equation is still practical. Speaking of high LCLs, does anybody recall conditions for the Wray, CO tornado earlier this year? I chased a couple storms closer to the front range that day, partially because they were closer to me, but also because I recall thinking DDs were rather large farther east. It did look like a pretty tall tornado in all the videos I saw.

 

[Jeff Duda]

Speaking of high LCLs, does anybody recall conditions for the Wray, CO tornado earlier this year? I chased a couple storms closer to the front range that day, partially because they were closer to me, but also because I recall thinking DDs were rather large farther east. It did look like a pretty tall tornado in all the videos I saw.

That storm formed right on the warm front/occluded warm/dryline front and so it's pretty much impossible to give much of a helpful range of the LCL height since it was right on a gradient between sky high LCLs (> 3000 m) and pretty low LCLs (< 1000 m). There are probably no observations that would answer that question since surface obs are pretty sparse in E CO. I seem to recall from photos and video however, that cloud bases weren't actually all that high.

 

[Dan Ross]

Well you may be the better judge on the height in the videos/photos, and that's a good point about the storm forming on the boundary between such vastly different air masses. Too bad every storm can't be surrounded by a mobile mesonet! I suppose another consideration may be how much a supercell modifies its own inflow. I suppose the cloud base could lower for a particular storm as it sucks up air from its RFD and FFD, given much of that air probably has a smaller DD and lower LCL.