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One-dimensional assimilation method for the humidity estimation with the wind profiling radar data using the MSM forecast as the first guess Jun-ichi Furumoto, Toshitaka Tsuda, Hiromu Seko, Kazuo Saito Introduction The turbulence echo power intensity with wind profiling radar is closely related with the refractive index gradient squared (M2), which is largely depends on the vertical humidity gradient in the moist atmosphere. Using the relations, humidity profiles can be estimated from a wind profiling radar data, if the sign of the radar-derived |M| is determined. Furumoto et al. (in print) has employed one-dimensional assimilation method to estimate humidity profiles with the MU radar-RASS measurements, complementary GPSderived precipitable water vapor and 12-hourly radiosonde results. Aiming at the estimation without simultaneous radiosonde data, this study estimates humidity profiles with a first guess from MSM forecast. Basic Principle of humidity estimation with wind profiling radar Specific humidity is derived from the relation between turbulence echo power and height potential of refractive index. | M | 1/ 2 N 1/ 3 M: Height potential of refractive index η: Echo power intensity N: Brunt-Vaisala frequency squared ε: Turbulence energy dissipation rate p N2 q N2 1 dq M K 0 K1 K2 T g T g T dz p: Pressure K0 ,K1 K2 : Constant q: Specific humidity z: Height g: Gravity acceleration rate 2 2 T 1 dT q( z ) 2 1.65 M 2 dz 02 q0 z0 p 7800 dz z : Potential temperature, Γ: Dry adiabatic lapse rate q0, θ0: Boundary value at the height of z=z0 •The time-interpolated radiosonde results are used as the boundary value at the height of z=z0 •The sign of the radar-derived |M| is determined to agree the integrated water vapour with GPS result and the constraint of time continuity of q. Variational method Variational method is a data assimilation technique to determine the most reasonable atmospheric state based on maximum likelihood estimation. The observation operator H, is defined to convert the atmospheric state vector to the observational one as: y Hx x: state vector consisting of the atmospheric state variables y: observation vector consisted of observed variables The analysis vector xa is determined as x when the conditional probability of x given the first guess (xb) and observation results (yo) has its maximum value. xa is obtained as x to minimize the cost function J(x) as : 1 1 J (x) = (x x b ) T B 1 (x x b ) + (y y o ) T R 1 (y y o ) 2 2 B: background covariance metrics R: observation covariance metrics If J(x) is differentiable, xa can be derived by minimizing J(x) using a quasi-Newton method. Expansion of 1D-Var for humidity estimation • • When the absolute value of |M| is assimilated directly into the background atmospheric state, J(x) has many local minima, and it is very difficult to find the global minimum using finite computer resources. To reduce the calculation cost of the assimilation, a new cost function was formulated by considering the statistical probability (Pr(z)) of the sign of |M|. Determination of sign of |M| 1 J (i ) 0.5 y (i ) y 0 (i) R 1 (i, i) y (i) y 0 (i) J1 (x) (x xb )T B 1 (x x b ) J o1 (x) 2 1 J ( i ) 0.5 y ( i ) y ( i ) R (i , i ) y ( i ) y 0 ( i ) 0 n J o1 (x) ln Pr(i) exp J (i) (1 Pr(i)) exp J (i) R-1(i,i) : the (i,i)-th component of R-1 i 1 Genetic algorithm (GA) is used to find the global minimum Pr(z) is calculated data from almost 1500 radiosondes launched since 1986. After the sign of M was determined, y0 after the previous step, is again assimilated using the general cost function. J 2 (x) = 0.5(x x0 )T B -1 (x x0 ) + 0.5(y y 0 )T R -1 (y y 0 ) The quasi-Newton method (BFGS method) is employed for the optimization Background and observation vector The variational method was applied to the assimilation of the MU radar-RASS observation results for the period from July 29 to August 5, 1999 x [ p0 , T0 , T1 ,..., TN 1,RH0 ,RH1,...,RH N 1 ] y [| M 0 |,| M1 |,...,| M N 1 |,IWVGPS ] p0: pressure at the lowest height. Ti: temperature at the j-th height RHi: relative Humidity at the j-th height IWVGPS: Integrated Water Vapor with GPS By assimilating the IWVGPS together with the radar-derived |M|, the signs of |M| are constrained. • The first guess of the atmospheric state vector was obtained from the MSM forecast obtained every hour. • The background error variances in the operational forecast model was used in this study. • The observational error variance was calculated from the statistics of the difference between the radar-derived M and MSM forecast. Observation error covariance (R) Histogram of the difference radar-derived M and radiosonde value • • • • thin solid: s.d. of the difference. thick solid: the s.d. of the difference approximated to the exponential function. dashed line: observation error of radiosonde measurement. dot dash line: observation error variance Time-height structure of specific humidity Balloon observation First guess from MSM Analysis Estimation with the forecast of prediction model The forecast of the operational Meso-Scale Model (MSM) of the Japan Meteorological Agency (JMA) used as the first guess, instead of the timeinterpolation of radiosonde data. The forecast error used at JMA is employed as the background error. . q profile Difference from radiosonde Bias error averaged for 6 profiles Dotted: MSM Black solid: analysis Red: radiosonde result Both bias and random errors in the analysis are smaller than these in the first guess. Random error averaged for 6 profiles 15LT Jul. 29, 2002 The discrepancy in the analysis is smaller than that in the first guess below 3.0 km. Conclusion Aiming at the precise estimation of humidity profiles with the wind profiling radar, the humidity estimation method with wind profiling radar data was developed. One-dimensional assimilation method was employed to determine the sign of the radar-derived refractive index gradient. The MSM forecast was used for the first guess of the assimilation algorithm. Time-height structure of humidity profile has successfully obtained with the MU radar-RASS measurement data. The retrieval results shows the improvement of precision from the first guess of MSM forecasts.