Analyses of in-situ hydrometeor measurements and what they imply - PowerPoint PPT Presentation

Analyses of in-situ hydrometeor measurements and what they imply about microphysical representations Z.S. Haddad Jet Propulsion Laboratory, California Institute of Technology

Example: Morrison-Thompson scheme • 5 species: CloudLiquid, CloudIce, Rain, Graupel, Snow • Gamma distribution for each species x : number of hydrometeors (per unit volume) whose diameter is between D and D + dD = N x D µ x e − Λ x D dD “intercept” “shape” “slope” Microphysics call: The model sends to the scheme (total number concentration, total mass concentration) for each species, along with the other prognostic variables, and the scheme then calculates conversion rates and amounts, and sends back to the model the new (number concentration, mass concentration) for each species 2

Example: Morrison-Thompson scheme • 5 species: CloudLiquid, CloudIce, Rain, Graupel, Snow • Gamma distribution for each species x : number of hydrometeors (per unit volume) whose diameter is between D and D + dD = N x D µ x e − Λ x D dD • For each species, µ x is given a priori, and the scheme ingests total number concentration N T and mixing ratio q and produces the corresponding N x and L x : Γ ( µ x + 1) Z N x D µ x e − Λ x D dD = N x N T = Λ µ +1 x and aD b N x D µ x e − Λ D dD = a N x Γ ( µ + 1) Γ ( b + µ + 1) Z mass ( D ) q = Λ µ +1 Λ b x Γ ( µ + 1) x 3

Example: Morrison-Thompson scheme • 5 species: CloudLiquid, CloudIce, Rain, Graupel, Snow • Gamma distribution for each species x : number of hydrometeors (per unit volume) whose diameter is between D and D + dD = N x D µ x e − Λ x D dD • For each species, µ x is given a priori, and the scheme ingests total number concentration N T and mixing ratio q and produces the corresponding N x and L x : Γ ( µ x + 1) Z N x D µ x e − Λ x D dD = N x N T = Λ µ +1 x and aD b N x D µ x e − Λ D dD = a N x Γ ( µ + 1) Γ ( b + µ + 1) Z q = Λ µ +1 Λ b x Γ ( µ + 1) x 4

Example: Morrison-Thompson scheme • 5 species: CloudLiquid, CloudIce, Rain, Graupel, Snow • Gamma distribution for each species x : number of hydrometeors (per unit volume) whose diameter is between D and D + dD = N x D µ x e − Λ x D dD • For each species, µ x is given a priori, and the scheme ingests total number concentration N T and mixing ratio q and produces the corresponding N x and L x : ◆ 1 /b ✓ a N T Γ ( b + µ x + 1) Λ x = q Γ ( µ x + 1) and Λ 1+ µ x x N x = N T Γ (1 + µ x ) 5

Example: Morrison-Thompson scheme • 5 species: CloudLiquid, CloudIce, Rain, Graupel, Snow • Gamma distribution for each species x : number of hydrometeors (per unit volume) whose diameter is between D and D + dD = N x D µ x e − Λ x D dD • For each species, µ x is given a priori, and the scheme ingests total number concentration N T and mixing ratio q and produces the corresponding N x and L x • µ CI = µ R = µ G = µ S = 0 ; µ CL = f ( N T ) (Martin et al, 1994) 6

Þ Assume G distribution: N ( D ) = N 0 D µ e −Λ D and let’s try to interpret the parameters in terms of physically meaningful quantities: ∫ D D 3 N ( D ) dD µ + 4 D m = = ∫ D 3 N ( D ) dD Λ µ + 1 3 ρ Γ ( µ + 1) D m $ ' 4 π D π ∫ q = ρ N ( D ) dD = N 0 & ) ( µ + 4) µ + 1 3 2 6 % ( 1/ 2 ( D − D m ) 2 D 3 N ( D ) dD % ( ∫ D m ' * σ m = = ' * ∫ D 3 N ( D ) dD µ + 4 & ) 7

Þ Assume G distribution: N ( D ) = N 0 D µ e −Λ D and let’s try to interpret the parameters in terms of physically meaningful quantities: ∫ D D 3 N ( D ) dD µ + 4 D m = = ∫ D 3 N ( D ) dD Λ µ + 1 3 ρ Γ ( µ + 1) D m $ ' 4 π D π ∫ q = ρ N ( D ) dD = N 0 & ) ( µ + 4) µ + 1 3 2 6 % ( 1/ 2 ( D − D m ) 2 D 3 N ( D ) dD % ( ∫ D m ' * σ m = = ' * ∫ D 3 N ( D ) dD µ + 4 & ) 8

Þ Assume G distribution: N ( D ) = N 0 D µ e −Λ D Special case: exponential distribution, i.e. µ = 0 µ + 1 3 ρ Γ ( µ + 1) D m $ ' 4 π D π ∫ q = ρ N ( D ) dD = N 0 & ) ( µ + 4) µ + 1 3 2 6 % ( πρ 24 N 0 D m = 9

Þ Assume G distribution: N ( D ) = N 0 D µ e −Λ D Special case: exponential distribution, i.e. µ = 0 24 D m = q πρ N 0 If, in addition, the intercept N 0 is assumed constant, this implies that D m / q = constant, and therefore • max( D m )/min( D m ) = max( q )/min( q ) • 10

Þ Assume G distribution: N ( D ) = N 0 D µ e −Λ D Special case: exponential distribution, i.e. µ = 0 24 D m = q πρ N 0 If, in addition, the intercept N 0 is assumed constant, this implies that D m / q = constant, and therefore • max( D m )/min( D m ) = max( q )/min( q ) • This is very dangerous, because it implies that in order to span a realistically large range of values of min( q ) < q < max( q ), we need to use a possibly unrealistic range of values of D m 11

Þ Assume G distribution: N ( D ) = N 0 D µ e −Λ D Special case: exponential distribution, i.e. µ = 0 24 D m = q πρ N 0 If, in addition, the intercept N 0 is assumed constant, this implies that D m / q = constant, and therefore • max( D m )/min( D m ) = max( q )/min( q ) • 3.5 mm / 0.5 mm ≠ 10 g/Kg / 0.1 g/Kg (in the case of rain) 7 << 100 !! 12

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Retrieved X from airborne radar data, using 2 forward operators: 1 from Kwajex microphysics and from 1 from COARE microphysics 100 (X kwajex – X coare )/X coare X = Rain rate X = D m Kwajex = 10-minute averages, COARE = 1-minute averages 15

Þ Assume G distribution: N ( D ) = N 0 D µ e −Λ D If, instead of assuming that the intercept N 0 is constant, the assumption is made that L is constant: ∫ D D 3 N ( D ) dD µ + 4 D m = = ∫ D 3 N ( D ) dD Λ 1/ 2 ( D − D m ) 2 D 3 N ( D ) dD % ( ∫ D m ' * σ m = = ' * ∫ D 3 N ( D ) dD µ + 4 & ) The above imply, regardless of whether µ is assumed constant or not: 2 / σ m 2 D m = D m D m 0.5 σ m = const D m , i.e. 2 = const ⇒ Λ σ m 16

(assumption: L constant) 1.5 ± noise Þ Unfortunately, in-situ observations say: σ m = const ⋅ D m 0.5 σ m ≠ const D m 17

(assumption: L constant) 1.5 ± noise Þ Unfortunately, in-situ observations say: σ m = const ⋅ D m 0.5 σ m ≠ const D m 18

What are these “in situ observations”? 1. Co-located 50 MHz + 0.92 GHz zenith-pointing profilers 19

What are these “in situ observations”? 1. Co-located 50 MHz + 0.92 GHz zenith-pointing profilers Example of VHF spectra from two consecutive height bins (Rajopadhyaya et al, J. Atmos. Ocean. Tech. 1998) 20

What are these “in situ observations”? 1. Co-located 50 MHz + 0.92 GHz zenith-pointing profilers Example 1: 17 December 2005, convective initiation and trailing stratiform 21

What are these “in situ observations”? 1. Co-located 50 MHz + 0.92 GHz zenith-pointing profilers Example 2: 27 December 2005, stratiform with some mild & shallow convection 22

What are these “in situ observations”? 1. Co-located 50 MHz + 0.92 GHz zenith-pointing profilers Example 3: 21 March 2006, convection reaching beyond the 10km cut-off ceiling 23

What are these “in situ observations”? 1. Co-located 50 MHz + 0.92 GHz zenith-pointing profilers 2. Joss-Waldvogel distrometer (ground) 24

What are these “in situ observations”? 1. Co-located 50 MHz + 0.92 GHz zenith-pointing profilers 2. Joss-Waldvogel distrometer 3. 2D-video distrometer 25

What are these “in situ observations”? 1. Co-located 50 MHz + 0.92 GHz zenith-pointing profilers 2. Joss-Waldvogel distrometer 3. 2D-video distrometer 4. Various airborne probes 26

What are these “in situ observations”? 1. Co-located 50 MHz + 0.92 GHz zenith-pointing profilers 2. Joss-Waldvogel distrometer 3. 2D-video distrometer 4. Various airborne probes Main problem for 2, 3 and 4: sampled volume (< 10cm x 10cm x 1000m) is, at best, over 5 orders of magnitude smaller than model resolution (> 1000m x 1000m x 100m) 27

What are these “in situ observations”? 1. Co-located 50 MHz + 0.92 GHz zenith-pointing profilers 2. Joss-Waldvogel distrometer 3. 2D-video distrometer 4. Various airborne probes 5. Polarimetric ground radar (volume-aggregated effect) Z HH = F 1 (N 0 , µ , L ) Z VV = F 2 (N 0 , µ , L ) 28

What are these “in situ observations”? 1. Co-located 50 MHz + 0.92 GHz zenith-pointing profilers 2. Joss-Waldvogel distrometer 3. 2D-video distrometer 4. Various airborne probes 5. Polarimetric ground radar (volume-aggregated effect) Z HH = F 1 (N 0 , µ , L ) Z VV = F 2 (N 0 , µ , L ) K dp = F 3 (N 0 , µ , L ; coefficients of oblateness relation) 29

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Why do the correlations matter? The model M is a complex (nonlinear) function which simulates the evolution of the state variables in time: dx t = M ( x t ) dt + N · db t But in reality dx t = M ( x t ; µ ) dt + N · db t M is very non-linear in µ – and yet models typically use one set of constant values (representing the mean), and ignore error bars (let alone any more realistic representations of the joint uncertainty in the components of µ ) In particular, how the uncertainty in x t depends on µ is difficult to represent 32