Formation and modelling of regional climate 19 June 2017 Department of Atmospheric Sciences, School of Resource Environment and Earth Science, Yunnan University, Kunming Formation and modelling of regional climate Hans von Storch Geesthacht, Hamburg, and 青岛

Scaling cascade and climate models

Formation of the general circulation on an aqua planet from a state of rest (from Fischer et al., 1991) Global climate

Continental climate Risbey and Stone (1996) Long term mean of - zonal wind at 200 hpa, and - band-pass filtered variance of 500 hpa geopotential height („storm track“) caused by planetary scale land-sea contrast and orographic features

Regional climate Composites of air pressure (left) and zonal wind (right) for day before intense precip in the Sacramento Valley (top), on the day of maximum precip (middle) Averaged over the ten most intense precip events. Risbey and Stone (1996)

Regional climates do not make up global climate. Instead, regional climate should be understood as the result of an interplay of global climate and regional physiographic detail. The local processes are important for the formation of the global climate not in terms of their details but through their overall statistics. Implications: Planetary scale climate can be modeled with dynamical models with limited spatial resolution The success on planetary scales does not imply success on regional or local scales. The effect of smaller scales can be described summarily through parameterizations.

Dynamical processes in a global atmospheric general circulation model 7

Climate = statistics of weather The genesis of climate Cs = f(Cl, Φs) with Cl = given by global simulations and global re-analyses Cs = smaller scale states or statistics Φs = parameters representative for regional features f = statistical or dynamical model  “downscaling”

Statistical downscaling: Determining statistics of impact variables von Storch, H. and H. Reichardt 1997: A scenario of storm surge statistics for the German Bight at the expected time of doubled atmospheric carbon dioxide concentration. - J. Climate 10, 2653-2662

The case of intra-seasonal storm-related sea level variations in Cuxhaven (at the mouth of the river Elbe) Annual percentiles of the approximately twice-daily hig-tide water levels at Cuxhaven after subtraction of the linear trend in the annual mean. From top to bottom, 99%, 90%, 80%, 50%, and 10% percentiles. Units are centimeters.

Canonical Correlation Analysis (CCA) One vector time series St is formed by the coefficients of the first four empirical orthogonal functions (EOFs) of winter [December–February (DJF)] monthly mean air pressure distributions. Prior to the EOF analysis, the air pressure data were centered; that is, the long-term mean distribution was subtracted so that anomalies were obtained. The other vector time series Qt is three-dimensional, featuring the 50%, 80%, and 90% percentiles of winter intra- monthly storm-related water-level distributions: Q = (q50%, q80%, q90%) The result of a CCA is pairs of vectors (ps;k, pq;k) and time coefficients as;k(t) and aq;k(t) so that St = k as,k (t) ps;k and Qt = k aq,k (t) pq;k Canonical Correlation Analysis (CCA) The coefficients as,1 and aq,1 have maximum correlation, the coefficients as,2 and aq,2 have maximum correlation after subtraction of the 1st components, and so forth The analysis describes which anomalous monthly mean large-scale pressure anomalies in winter over the North Atlantic are associated with which intra-monthly anomalies of 50%, 80% and 90% percentiles of storm water variations at Cuxhaven

First two characteristics patterns ps;1 (top) and ps;2 (bottom) of monthly mean air pressure anomalies over the northeast Atlantic. The coefficients of these CCA vectors share a maximum correlation with the coefficients of the water-level percentile patterns given on the right. Units are hPa. Time series of 90% percentiles of intra-monthly storm-related water-level variations in Cuxhaven, as derived from in situ observations (solid) and estimated from the monthly mean air pressure field (dashed).

Statistical downscaling: Generating time series through conditional weather generators Busuioc, A., and H. von Storch, 2003: Conditional stochastic model for generating daily precipitation time series, Clim. Res. 24, 181-195

Rainfall as a 2-state first-order Markov chain A „rainfall generator“ is a stochastic process, which mimics the behavior of rainfall as a sequence of either „wet“ or „dry“ days. A specific rainfall generator makes use of four parameters: The probability to have wet day following another wet day Prob(wt|wt-1) = p11 Then Prob(dt|wt-1) = 1-p11 The probability to have wet day following a dry day Prob(wt|dt-1) = p01 Then Prob(dt|dt-1) = 1-p01 c) The amount of rainfall on a „wet“ day is described by a  -distribution (k,θ) with „shape“ parameter k and „scale“ parameter θ. Rainfall as a 2-state first-order Markov chain The four parameters are p11 , p10 , k , and  = k θ (the mean). They can be estimated from the data.

Patterns of the first CCA pair of winter mean SLP and winter parameters of precipitation distribution derived from the first half of the observations (1901–1949)

Dynamical downscaling: Regional models as downscaling tool

Regional atmospheric modelling: nesting into a global state

global model variance Spatial scales Insufficiently resolved Well resolved Spatial scales

regional model variance Spatial scales Added value Insufficiently resolved Well resolved Spatial scales Added value

A mathematically well-posed problem is achieved when the task of describing the dynamics of determining regional and smaller scales is formulated as a state space problem, which is conditioned by large scales. Physically, this means that genesis of regional climate is better framed as a downscaling problem and not as a boundary value problem.

Known large scale state RCM Physiographic detail 3-d vector of state Known large scale state projection of full state on large-scale scale Large-scale (spectral) nudging

Expected added value Statistics and events on scales, which are not well resolved for the global system, but sufficiently resolved for the regional model. In particular, increased variance on smaller scales. No improvement of the dynamics and events on scales, which are already well done by the global system

Improved presentation of in coastal regions ERA-I-driven multidecadal simulation with RCM CCLM over East Asia (李德磊, 2015) Grid resolution: 0.06o Employing spectral nudging (wind above 850 hPa, for scales > 800 km) Usage of Quikscat-windfields (QS) over sea as a reference Considering ratios 2QS:2ERA and 2QS:2RCM Determining Brier Skill score for all marine grid boxes B = 1 – (RCM-QS)2 / (ERA-QS)2

QuikSCAT/ ERA I-reanalysis Quikscat/ CCLM regional simulation 李德磊, 2015

QuikSCAT: Added Value – Brier skill score vs. ERA Open Ocean: No value added by dynamical Downscaling in terms if Brier Skill score. Coastal region: Added Value in complex coastal areas Hier sehen wir für die selben Stationen die Perzentil-Perzentil Plots für QuikSCAT. Die Ergebnisse werden am Ende zusammengefasst, jetzt gehe ich auf den zweiten Schwerpunkt der Arbeit ein. 李德磊, 2015

Coastal stations Offshore stations Comparison of CCLM (left-panel, y-axis) and ERA-I (right-panel, y-axis) wind data with observations from two coastal stations and two offshore wind observations (x-axis). Scatter plots (grey dots), qq-plots and several statistical measures (李德磊 , 2015)

Improved representation of sub-synoptic phenomena NCEP-driven multidecadal simulation with RCM CLM over North Pacific (陈飞 et al., 2012, 2013, 2014) Grid resolution: about 0.4o Employing spectral nudging (wind above 850 hPa, for scales > 800 km) Simulation of sub-synoptic phenomena Polar lows in the Northern North Pacific

Annual frequency of past polar lows in the North Pacific Number of detected Polar Lows in the North Pacific per Polar Low season (PLS; October to April). The trend from 62 PLSs, from 1948/1949 to 2009/2010, amounts to 0.17 cases/year. 陈飞 et al., 2013

Scenarios of Polar Low Formation in the North Pacific A1B_1: -0.29 A2_1: -0.49 陈飞 et al., 2014

Improved representation of forcing fields for impact models NCEP-driven multidecadal simulation with RCM REMO in Europe Grid resolution: 0.5 o Employing spectral nudging (wind above 850 hPa, for scales > 800 km) 1948-2010 simulation Wind and air pressure used to drive models of sea level and circulation of marginal seas (not shown) for describing currents and sea level Wind used to drive models of the statistics of surface waves (ocean waves) in coastal seas (North Sea).

Extreme wind events simulated compared to local observations simuliert These plots are the quantile-quantile diagrams (REMO & NCEP Vs Observations) for 10-m wind speed at 2 buoys station. The first one is an Atlantic offshore buoy (ZBGSO, located at 48.7N,12.40W), already assimilated by NCEP. The second one shows results from a Mediterranean buoy (ZATOS, located at 39.96N, 24.72E, Aegean Sea), whose data have NOT been previously assimilated by NCEP. Weisse, pers. comm.

Red: buoy, yellow: radar, blue: wave model run with REMO winds significant wave height [days] wave direction [days] Red: buoy, yellow: radar, blue: wave model run with REMO winds Gerd Gayer, pers. comm., 2001

Global Downscaling with global AGCM, spectrally nudged to NCEP reanalysis. Added value generated in complex coastal and mountaineous regions (in red). Global distribution of Brier Skill Score, comparing the global downscaling data with the driving NCEP1 re-analysis, for 6 hourly 10m wind speed for the decade 1999 (Dec) - 2009 (Nov). ERA-Interim re-analysis data are used as reference. The diurnal cycle has been taken out. Contour interval: 0.2. Von Storch, et al., 2017, submitted

Conclusion … Downscaling (Cs = f(Cl,Φs)) works with respect to atmospheric dynamics – ocean dynamics: needs more analysis. Several options, - statistical downscaling, generating characteristics of distributions and processes, such as monthly means, intra-monthly percentiles, parameters of Markov processes etc. - dynamical downscaling using „state-space“ formulation of large-scale constraining (spectral nudging) Added value on - medium scales (in particular coastal regions and medium scale phenomena (in particular storms) - in generating regional impact variables, in particular wind for storm surges and ocean waves. Downscaling allows the generation of homogeneous data sets (i.e., data sets of uniform quality across many decades of years)