# Presentation: 524094

## Modeling the atmospheric boundary layer: models, their limitations and observations

- William R. Cotton
- Dept of Atmospheric Science
- Colorado State University

## Outline of talk

- Types of Models
- The convective ABL
- The cloudy ABL
- The Stable ABL
- Heterogeneities in the BL
- Observation Biases

## Shape of a growing thermal.

## Formation of a thermal bubble.

## Slide 5

## Longitudinal cells with helical motions (also called “rolls,” “streets,” “lines,” “bands,” and “strips”).

## Features of Cloud Streets

- Lengths 20 to 500 km.
- Spacing between bands 2 km to 8 km.
- Width/height _~_ 2 to 6.
- Vertical shear:  10-7 to 10-6 cm-1 s-2.

## Conditions Favoring Cloud Streets

- High winds in the boundary layer.
- A relatively unidirectional wind profile that is curved (exhibits a maxima in the BL).
- A cloud layer that is convectively unstable.
- In terms of mixed layer scaling, when 3 ≤ h/L ≤ 10:  where h is the BL depth and
- 	(the Monin-Ubukhov length).

- _Other features of cloud streets_:
- Lengths:  20 to 500 km
- Spacing between bands:  2 to 8 km
- Depth of BL:  0.8 to 2 km
- Width/height:  2 to 7
- Vertical shear of horizontal wind:  10-7 to 10-6cm-1s-1

## Slide 9

## Types of Boundary Layer Models

- Mixed layer models
- Eddy viscosity models
- Closure models
- LES models

## Mixed Layer Models

- Basic assumption is that conserved variables (theta, total water) are constant within a mixed layer.

## Stull, R.B., 1988:  An Introduction to Boundary Layer Meteorlogy, Kluwer Academic Publishers, Dordrecht, The Netherlands.

## Deficiencies of Mixed Layer Models

- Entrainment rates are often modeled to be a small percentage of flux from the surface.
- When wind shear is present it can vary in a non-predictable manner.
- The nocturnal BL is often not well-mixed so these models are often not appropriate.
- Under certain conditions the BL can be multi-valued; an example is here along the Front Range where a plains BL develops separate from a mountain BL, which advects over the plains BL. Soaring example.

## Eddy Viscosity Models

## Reynold’s Averaged Equations 

- of Motion

- Eddy viscosity Closure:

- For scalars:

## Deficiencies of K-theory models

- In the mixed layer where gradients of conservative variables are zero, infinite K’s would be required. Instead these models maintain gradients in the BL even though they should be small or absent.
- Under certain situations counter-gradient fluxes occur and turbulence is non-local.

## Higher Order Closure Theory

**Aim:  **To form predictive equation on 	       , the Reynold’s stress:

- For TKE =e

- Mech. Prod.

- Buoy.

- Turb. Temp.

- P-diffusion

- Dissipation

- Local change

- Advection

## To close 2nd-order equations, form:

- equation and so forth or use simple closure model on 3rd-order terms.

## Why predict TKE?

- Use full information for sub-grid scales, e.g.

- Information for parameterizing microphysical forcing on sub-grid scales:

- P

## Most Boundary-Layer Parameterizations Are Tuned and tested with Golden Day Data;Day 33 Wangara!

## A PDF-based closure model of the cloud boundary layer developed and tested using LES data acquired with GCSS case studies

## Approach

- Represent the subgrid-scale variability of vertical velocity, temperature, and moisture using a joint probability density function (PDF).

- Predicting the full subgrid-scale PDF is computationally too expensive, so we need to identify a suitable family of PDFs.

## Approach

- General foundation.
- Testable empiricism.
- Consistency:
- PDF can be used to diagnose cloud properties and higher-order turbulent moments.
- No trigger function required.

- Some advantages of the assumed PDF method:

## PDFs of boundary layer clouds

- What do PDFs of boundary layer clouds actually look like?
- PDFs have been analyzed from:
- Aircraft measurements from ASTEX and FIRE experiments.
- Three dimensional large-eddy simulations (LES) using the Regional Atmospheric Modeling System (RAMS).
- As an example, let’s look at results from a  LES of cumulus clouds over land.

## What is a LES?

- Very fine grid spacing typically 50m or less in horizontal and 25m or less in vertical.
- This permits explicit resolution of the dominant energy-containing eddies in the BL.
- Closure is sub-grid scale and since scales of unresolved motions are very small, it is thought that the models are not sensitive to the closure assumptions.

## PDFs of cumulus clouds

- Isosurface of cloud water:  0.001 (g/kg)

## PDFs of cumulus clouds

- Isosurface of cloud water:  0.001 (g/kg); horizontal cross section a = 1680 (m)

## PDFs of cumulus clouds

- Horizontal cross section of vertical velocity; z=1680(m)

## PDFs of cumulus clouds

## Example of a PDF fit

## Evaluations of the PDFs

## Constructing a parameterization using the assumed PDF method

## Building a PDF closure scheme

- Parameterization developed in a single-column model framework.
- Use LGC double Gaussian family of PDFs for the sub-grid scale.
- Use averaged advection-diffusion equations to predict means and turbulent moments.
- Initialize with mean profiles of winds, temperature, moisture.
- Integrate in time and space (height).
- Diagnose PDF parameters for each grid box and timestep.

## Building a PDF closure scheme

- Advance prognostic equations for low-order moments:
- Diagnose PDF parameters using the prognosed moments:
- Close higher-order moments using PDF:
- Compute cloud fraction and cloud water from PDF.

## BOMEX:  trade-wind cumulus

- Time evolution of cloud fraction:

-   LES

-   Single-Column

## BOMEX:  trade-wind cumulusProfiles of cloud fraction and cloud water.

## ARM:  cumulus over land

- Time evolution of cloud fraction:

-   LES

-   Single-Column

## ARM:  cumulus over landProfiles of cloud fraction and cloud water.

## FIRE:  stratocumulusProfiles of cloud fraction and cloud water.

## ATEX:  Cu under SC

- Time evolution of cloud fraction:

-   LES

-   Single-Column

## ATEX:  Cu under ScProfiles of cloud fraction and cloud water.

## Limitations of closure models

- Very fine vertical grid spacing is needed to calculate vertical gradients and fluxes.
- Except for M-Y TKE model where only one prognostic equation is added to the mean variables, models which predict cloud coverage and average cloud properties add something like 10 additional forecast variables (i.e., costly).
- Required time steps are shorter than used in most NWP forecast models. Time-splinting offers one way to overcome that.

## Limitations of LES Models

- They are far too costly for use in operational NWP models; but as shown above they can be useful in developing and testing models suitable for operational use.
- In spite of underlying assumptions they are sensitive to sub-grid closures.
-  This is particularly true near the surface and near a capping inversion where “large eddies” are not predominant.

## Inferences from soaring the convective boundary layer

- Poor prediction of cloud cover either within the boundary layer or above BL levels such as cirrus, Cb anvils, and lenticular is the biggest source of BL forecast errors.
- The BL over the Colorado Plains is often multi-valued. The plains BL may cap at 3000’ AGL with virtually no thermals until 5000’ to 6000’ where the mountain BL advects over the plains. Since I have a motor (cheat!) I often power through the intervening stable layer, connect into the upper BL and fly for many hours up to 14,000’AGL where motorless planes are stuck to low-levels.
- The MY-TKE model is a better predictor of BL depth even when it is single-valued than mixed layer models; but it does not give an explicit value it instead has to be inferred from small magnitude TKE at its top.
- Thermals in the mountains are often big and strong, but widespread compared to the plains and are often associated with well-defined hot spots (rocks!).
- Thermals over the plains are often more homogeneous but certain hotspots like feedlots and irrigation no-irrigation boundaries are good thermal sources.

## Slide 45

## Slide 46

## Slide 47

## Slide 48

## Slide 49

## The stable boundary layer

- When Ri is greater than 0.2, surface fluxes are not adequately described by Monin-Obukhov similarity theory which is in widespread use in numerical models.

## Slide 51

## Slide 52

## Characteristics of the stable BL

- It is characterized by intermittent turbulent bursts at intervals of 10’s to 1000’s of seconds.
- Contributors to intermittency include, but are not limited to, density currents, solitary waves, roll vortices, K-H billows, elevated ducted layers, katabatic flows, residual elevated turbulence penetrating downward, physiographic heterogeneity, orographic waves, and inertial oscillations.

## Symptoms of inadequate representation of fluxes is excessive surface cooling due to: 

- Strong surface radiative cooling which strengthens inversion.
- Near-surface flow thereby accelerates but shear is reduced above where turbulence operates.
- Increased near-surface flow increases surface heat flux causing more cooling, but reduced shear above reduces turbulent flux of warm air downward.

## Poulos and Burns (2003) propose

- Add a random variable to friction velocities, etc, in which the PDF is derived from experimental data around the globe during all seasons.

## Mesoscale variability of the ABL

## Slide 57

## Conceptual model of the regional-scale daytime circulation system over the north-central Colorado Rocky Mountains.

## The Urban BL

## Regional Land-Use Change Effects on Climate in the Summer

**From: Marshall, C.H. Jr., R.A. Pielke Sr., L.T. Steyaert, and D.A. Willard, 2004: The impact of anthropogenic land cover change on warm season sensible weather and sea-breeze convection over the Florida peninsula. ***Mon. Wea Rev***., 132, 28-52.**

## Slide 61

## Slide 62

## Slide 63

## Slide 64

## Two-month average of the surface latent heat flux (W m-2) from the model simulations of July and August 1994 with pre-1900s land cover (top), 1994 land use (middle), and the difference field for the two (bottom; 1994 minus pre-1900s case).

**Two-month average of the surface latent heat flux (W m****-2****) from the model simulations of July and August 1994 with pre-1900s land cover (top), 1994 land use (middle), and the difference field for the two (bottom; 1994 minus pre-1900s case).**

## Slide 66

## Slide 67

## Some Examples of Temperature Sensor Bias

## The following slides are taken from:

- Hanamean, J.R. Jr., R.A. Pielke Sr., C.L. Castro, D.S. Ojima, B.C. Reed, and Z. Gao, 2003: Vegetation impacts on maximum and minimum temperatures in northeast Colorado. *Meteorological Applications*, **10**, 203-215.
- Davey, C.A., and R.A. Pielke Sr., 2004: Microclimate exposures of surface-based weather stations - implications for the assessment of long-term temperature trends.** ***Bull. Amer. Meteor. Soc*.,** **in press**.**

## Photographs of the temperature sensor exposure characteristics of the NWS COOP station at Lamar, Colorado. Panel a) shows the temperature sensor, while panels b)-e) illustrate the exposures viewed from the temperature sensor looking N, E, S, and W, respectively. 

- Photographs of the temperature sensor exposure characteristics of the NWS COOP station at Lamar, Colorado. Panel a) shows the temperature sensor, while panels b)-e) illustrate the exposures viewed from the temperature sensor looking N, E, S, and W, respectively.

## Photographs of the temperature sensor exposure characteristics of the NWS COOP station at Las Animas, Colorado. Panel a) shows the temperature sensor, while panels b)-e) illustrate the exposures viewed from the temperature sensor looking N, E, S, and W, respectively. 

- Photographs of the temperature sensor exposure characteristics of the NWS COOP station at Las Animas, Colorado. Panel a) shows the temperature sensor, while panels b)-e) illustrate the exposures viewed from the temperature sensor looking N, E, S, and W, respectively.

## MMTS installation near John Martin Reservoir, Colorado. 

- MMTS installation near John Martin Reservoir, Colorado.

## Figure 11:  Fort Morgan site, showing images of the cardinal directions from the sensor.

## Summary

- Models of the ABL used in operational forecast models remain relatively crude
- Cloud cover forecasts are the biggest source of error in BL forecasts due to both above BL clouds and clouds within the BL
- The nocturnal boundary layer is poorly handled by all BL models including LES models
- The BL is often characterized by active mesoscale circulations that include rolls, sea-breeze, heat island, and land-use thermally-driven circulations, mountain slope flows and density currents and bores
- Care must be taken in interpreting surface observations owing to siting problems