Estimation of temperature and humidity with a wind profiling radar-RASS measurements Toshitaka Tsuda Research Institute for Sustainable Humanosphere, Kyoto University

Estimation of temperature and humidity with excellent temporal and height resolutions is important for elucidation of thermo-dynamical mechanism of severe meteorological phenomena. RASS technique enable to observe these parameters regardless of weather conditions. Wind velocity ← Wind Profiling radarWind velocity ← Wind Profiling radar Temperature ← RASSTemperature ← RASS Humidity ← RASSHumidity ← RASS Introduction

Basic principle of RASS technique RASS: Radio Acoustic Sounding System ・ Relationship between acoustic velocity (c s ) and atmospheric virtual temperature(T v ) Wind profiling radar Transmitted radio wave Acoustic wavefront RASS echo Speaker Acoustic velocity The Bragg condition is required to obtain strong RASS echo :acoustic wavenumber vector :radio wavenumber vector The Bragg condition is required to obtain strong RASS echo :acoustic wavenumber vector :radio wavenumber vector K d =20.047

Temperature Observation with the MU radar-RASS Timings of radiosonde launch Hyperbolic horn speaker

・ Detailed structure of Cold front observed with the MU radar-RASS

NICT Okinawa Subtropical Environment Remote Sensing Center, Ogimi Wind Profiler Facility (128.16E, 26.68N) Temperature Observation in the Okinawa subtropical region 443MHz wind profiling radar Typical wind direction Spring Autumn Summer Transmission Power p-p 20 kW Ave. 2 kW Pulse width 1.33, 2.0, 4.0  m Beam steering5 beams; Vertical and north, east, south, west steered to 10.5 degree Winter Radar Antenna Portable horn Fixed horn Baiu front and Severe Typhoon frequently passed over Okinawa Subtropical region

(℃)(℃) Height (km) RASS echo Doppler Velocity (m/s) 気温の時間高度分布 Inversion Layer Virtual temperature( ℃ ) Height (km) Time 2006 年 11 月 Radiosonde RASS Observation of Inversion Layer Nov. 8, 2006Nov. 9, 2006

q : Potential temperature, Γ: Dry adiabatic lapse rate q 0, θ 0 : Boundary value at the height of z=z 0 p: Pressure q: Specific humidity g: Gravity acceleration rate M: Height potential of refractive index η: Echo power intensity N: Brunt-Vaisala frequency squared ε: Turbulence energy dissipation rate K 0, K 1 K 2 : Constant z: Height Specific humidity is derived from the relation between turbulence echo power and height potential of refractive index. Humidity profile can be estimated if the sign of the radar-derived |M| is determined by incorporating data of other instruments (i.e. precipitable water vapour by ground-based GPS receiver) Basic Principle of Humidity Observation with Wind Profiling radars: Retrieval of Humidity Profiles with the wind profiling radar

The MU Radar-RASS and GPS observation in July, , with s.d. of 0.07 Humidity Profiles obtained with the MU radar-RASS measurements Radiosonde data at z0=7.5 km, where the SNR was fairly high and time variation of q was sufficiently small was used as the boundary value.  0, q 0, p were derived from time-interpolation of radiosonde soundings. 15LT 21LT 03LT 09LT 15LT The radar data were averaged for 30 minutes.

The MU radar + LTR Solid: Radiosonde result Dotted: Radar estimate |M||M| q The difference below 2 km seems to be due to the large variation of humidity in the upper boundary layer. Radiosonde The timing of radiosonde observation used for the humidity estimation with wind profiling radars. The timing of radiosonde observation not used for the estimation. Application to the boundary layer radar data

EAR Location Koto Tabang, Indonesia (0.20°S, °E) Center freqency: 47.0MHz Peak power : 100 kW Antenna diameter 110 m Application to the equatorial atmosphere radar Height (km) (AGL) Nov LST The difference averaged for 51 comparisons. Nov LSTNov LSTNov LST Dotted line: EAR Solid line: radiosonde The mean difference is within 1 g/kg.

Humidity Profiles obtained with the MU radar-RASS Radiosonde First Guess Analysis The analysis successfully retrieved detailed humidity variations that cannot be expressed by the first guess. Humidity Estimation using 1D-Var algorithm Aiming at more precise estimation of humidity profiles, A new algorithm to determine the sign of M by applying a one- dimensional variational method was developed. Time-interpolated radiosonde results along 12 hour was employed as the first guess The GPS-derived PWV is simultaneously assimilated to constrain the sign of |M|.

Conclusion Temperature and humidity retrieval algorithm with wind profiling radar was presented. Temperature profiles can be estimated by combining wind profiling radar and acoustic source. –The MU radar-RASS can measure temperature profiles below the lower stratosphere with a temporal and height resolution of a few minutes and 150 m. –The RASS technique was applied to the 443MHz wind profiling radar in Okinawa subtropical region, aimed to monitor the detailed thermo-dynamic structure of severe meteorological phenomena. Humidity profile is estimated from the turbulence echo characteristics. –Overall structure of the radar-derived q agrees well with the radiosonde result. The radar result shows the detailed structure of humidity, which cannot be resolved by radiosonde results. –The retrieval method developed with the MU radar was successfully applied to the L-band wind profiling radar and Equatorial Atmosphere Radar. –The new retrieval algorithm was also presented and used one-dimensional variational method that determines the sign of radar-derived |M|. Conclusions

fin

The analysis vector x a is determined as x when the conditional probability of x, given the first guess (x b ) and observation results (y o ), attains its maximum value. Generally, x a is obtained as x to minimize the cost function J(x): B: covariance matrices of x b R: covariance matrices of y o One of major data assimilation method based on the most likelihood estimation. x: n-element state vector y is the observation vector The Variational Method: The observation operator H, used to convert the atmospheric state vector to the observational one, is defined as

Application for Humidity Estimation with Wind Profiling radars State and Observation Parameters By assimilating the IWV G together with the radar-derived |M|, the signs of |M| are constrained. The variational method is applied to the assimilation of MU radar/RASS observation results for the period July 29 to August 5, The first guess value was calculated from linear interpolation of radiosonde data. Diagram used to calculate the first guess T i : Tempearture R i : Relative Humidity IWV GPS : Integrated Water Vapor with GPS e s : Saturated water vapor pressure

After the sign of M was determined, y o after the previous step, is again assimilated using the general cost function. The BFGS method was employed for the optimization. When the absolute value of |M| is assimilated directly into the background atmospheric state, J(x) has many local minima. The number of the local minima in J(x) is as large as 2 l, where l is the number of height layers of the observation. 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|. Cost function with considering the ambiguity of sign of |M| R(i,i) : the (i,i)-th component of R Genetic algorithm (GA) is used to find the global minimum

Pressure Temperature RH S.d. of the difference between the first guess and the radiosonde results ( D x diff ) The background error ( D x b ) (doted dashed) is derived by removing the instinct sensor error of the radiosonde ( D x s ) (dashed) from D x diff (solid). The background error calculated from 12-hourly radiosonde results. B from 6-, 12-, 18-, and 24- hourly interval radiosonde results Background Error Covariance Matrix (B)

The observational errors covariance matrix (R) is calculated from the s.d. of the differences between M from the radiosonde and radar measurements. Assuming independence of the observation errors of radar and radiosonde, the observation error was calculated by subtracting the radiosonde instinct error from the results of the least-squared method. Thick solid ： Approximated line of s.d. of the difference. Dashed: Instinct error of radiosonde Dot-dashed ： Observation Error Variance Observation Error Covariance (R)

Black solid ： radiosonde, Black dashed ： first guess Red ： analysis Black ： first guess Red ： analysis result Blue ： conventional method In all figures analysis is in good agreement with radiosonde results. This demonstrates that the variational method can retrieve precise humidity profiles, especially below 4.0 km height where rapid variations in humidity are large, even in the large background error. Error of analysis due to the precision of first guess q profiles are derived from the first guess calculated from 6-, 12-, 18-, and 24-hourly radiosonde results Humidity Profiles 6hr12hr18hr24hr Averaged random error profile