1. D. C. Stolz, S. A. Rutledge, J. R. Pierce, S. C. van den Heever 2017
A global lightning parameterization based on statistical relationships among environmental factors, aerosols, and convective clouds in the TRMM climatology
D. C. Stolz, S. A. Rutledge, J. R. Pierce, S. C. van den Heever
2017

2. 3 Objectives
Inputs: normalized CAPE (NCAPE), cloud-condensation nuclei (CCN), warm cloud depth (WCD), vertical wind shear (SHEAR), relative humidity (RH)
Outputs: total lightning density (TLD), average height of 30dbz echoes (AVGHT30)
1) Can the inputs predict the outputs? 2) Do combinations of the inputs predict the outputs better than the inputs themselves? 3) What is the influence of each input on the outputs when we control the other inputs?

3. TRMM Dataset Tropical Rainfall Measuring Mission (TRMM): 2004-2011
Precipitation Radar (PR)
Lightning Imaging Sensor (LIS)
Convective feature (CF) = convective region defined by 2A23 algorithm
Lightning producing CF (LPCF) = when LIS detects a lightning flash above the min. threshold of 0.7 flashes/min
Vertical profile of radar reflectivity (VPRR):
determined by 2A25 algorithm
used to find AVGHT30 = peak altitude in mean VPRR when the reflectivity is dBZ
CFs filtered for deep convection, when AVGHT30 > 5 km
~1.4 million CFs and >250,000 LPCFs documented

4. GEOS-Chem and ERAi Datasets
GEOS-Chem: chemical transport model used to estimate…
CCN – number concentration of aerosols with diameter > 40nm
*Used model data to avoid issues with aerosol detection from satellites (uncertainties and cloud obscuring)
ERAi: reanalysis data used to estimate…
NCAPE – mixed layer pseudoadiabatic CAPE/depth of positive area in sounding
*positive bias in surface moisture in ERAi, but still the best reanalysis for convective clouds
WCD – difference in the 0°C isotherm and LCL
SHEAR – hPa vertical shear
RH – average RH hPa
Inflow swath for CCN
GEOS-Chem and ERAi data were linearly interpolated to the time of TRMM overpass for each CF

5. General Regression Behavior
Linear and logarithmic runs for inputs and combinations of inputs over globe and different regions
R2 < 0.3 for single inputs
CCN logarithmic model R2 up to 0.6
SHEAR model R2 < 0.1
Model with all 5 inputs performs better
Logarithmic generally better than linear
Do the models have constant error covariance and Gaussian residuals (consistent with assumptions of multiple-linear regression)?
Linear: errors increase with higher output values = BAD
Log: uniform errors across output values, centered around 0 = GOOD
As a result, will focus on logarithmic model with all inputs

6. Relative Importance of Inputs on Outputs
Increase in Global TLD and AVGHT30:
↑ NCAPE, ↑ CCN, ↓ WCD, ↑ SHEAR, ↓ RH
CCN typically has largest weight
SHEAR has smallest weight
Generally low shear in tropics because of weak horizontal temperature gradients
Minimum in RH increases convective activity by modifying downdrafts and producing secondary convection
RH more important in smaller regions of CNG and AMZ
0.71 < R2 < 0.81
0.68 < R2 < 0.78
AMZ TLD R2 = 0.82, CNG TLD R2 = 0.68
AMZ AVGHT30 R2 = 0.74, CNG AVGHT30 R2 = 0.68

7. Regional Distribution of Inputs and Outputs
TLD and AVGHT30 maximized over continents, similar between hemispheres
All regions have similar NCAPE, WCD, SHEAR, RH and inputs are realistic for deep tropical convection
More than 10,000 CFs for each region so good representation
Large difference in CCN distributions:
CCN are dominant factor when transitioning from pristine to polluted env.
Weight of CCN less in constantly polluted env. (except CNG)

8. Global Lightning Parameterizations
Probability of lightning: global = 11.9%, continental = 30.8%, oceanic = 5.3%
log 10 TLD =c+ w NCAPE log 10 NCAPE + w CCN log 10 CCN − w WCD log 10 WCD + w SHEAR log 10 SHEAR − w RH log 10 RH
Global approximation
Underestimates TLD over continents
Overestimates TLD over ocean
Average difference between observed and approx. is 21.6%
Hybrid approximation
Reduces biases over globe
Average difference between observed and approx. is 11.6%
Differences in oceanic and continental convection makes a universal lightning parameterization unreliable

9. Summary
Left:
Deep WCD, low CCN, small NCAPE, little shear, moist mid-levels, small TLD, lower AVGHT30
Weak updrafts don’t loft graupel and supercooled water up
Low CCN promote warm rain processes
Deep WCD results in more narrow cloud base so more entrainment
Right:
Shallow WCD, high CCN, large NCAPE, higher shear, lower moisture in mid- levels, large TLD, higher AVGHT30
Larger NCAPE means ‘more explosive vertical motions’
High CCN reduce size of particles which inhibits warm rain processes